It is sardonic, in the sense of "skeptically humorous". You would expect someone to know what his own point is. Another indication is that the humor is directed at himself. Sarcastic remarks are usually directed at someone or something else.

Sarcasm is closely related to irony, and a sarcastic remark is intended to hurt or insult someone.

• Oxforddictionaries.com: the use of irony to mock or convey contempt. (http://www.oxforddictionaries.com/us/definition/american_english/sarcasm)

• Merriam-Webster: a sharp and often satirical or ironic utterance designed to cut or give pain. 2a) a mode of satirical wit depending for its effect on bitter, caustic, and often ironic language that is usually directed against an individual. (http://www.merriam-webster.com/dictionary/sarcasm)

• Collins English Dictionary: mocking, contemptuous, or ironic language intended to convey scorn or insult. (http://www.dictionary.com/browse/sarcasm)

• Random House Dictionary: 1) harsh or bitter derision or irony. 2) a sharply ironical taunt; sneering or cutting remark. (http://www.dictionary.com/browse/sarcasm)

• The American Heritage New Dictionary of Cultural Literacy: A form of irony in which apparent praise conceals another, scornful meaning. (http://www.dictionary.com/browse/sarcasm)

Sardonic is also derisive, and potentially involves irony, but it is mostly characterized by grimness, cynicism, or skepticism.

• Oxforddictionaries.com: Grimly mocking or cynical. (http://www.oxforddictionaries.com/us/definition/american_english/sardonic)

• Merriam Webster: disdainfully or skeptically humorous: derisively mocking. (http://www.merriam-webster.com/dictionary/sardonic)

• Random House Dictionary: characterized by bitter or scornful derision; mocking; cynical; sneering. (http://www.dictionary.com/browse/sardonic)

• Online Etymology Dictionary: "apparently but not really proceeding from gaiety...of bitter or scornful (laughter)..." from a plant called sardonion, which caused the face to contort in a way resembling sardonic laughter, usually followed by death. (http://www.etymonline.com/index.php?term=sardonic)

The audience for a sardonic remark is the self, whereas a sarcastic remark is directed at a victim.

See the table regarding types of humor at http://www.etymonline.com/index.php?term=humor&allowed_in_frame=0 (H.W. Fowler, "Modern English Usage," 1926.)

Since the example sentence is aimed at Barry himself, and it is not an ironic statement, it is best characterized as sardonic, rather than satirical.

Given that the author is Dave Barry, I believe the example sentence is neither. I would call it mildly self-effacing humor.

It isn't sarcasm:

"the use of words that mean the opposite of what you really want to say especially in order to insult someone, to show irritation, or to be funny"

http://www.merriam-webster.com/dictionary/sarcasm

Dave really means (in earnest) that he isn't clear on what his point is. He is not saying the opposite of what he means, he's saying exactly what he means.

It also isn't sardonic:

"showing that you disapprove of or do not like someone or something : showing disrespect or scorn for someone or something"

http://www.merriam-webster.com/dictionary/sardonic

Dave does not seem to disapprove or dislike the fact that he isn't 100% certain on what his point is. There is not any sign of disrespect or scorn in his statement. He seems perfectly comfortable with his own uncertainty. The fact that he isn't certain on what his point is, is of no real concern to him. His statement lacks the requisite degree of bitterness to be termed sardonic.

I can relate (as I'm sure can many) to his sentiment. I think many of us less gifted in Dave's brand of modest humor would have said simply "I digress". Have you ever started to talk about something no longer at the heart of the matter at hand, but gone so far down that path that you no longer clearly remember what the heart of the matter was in the first place? That's what Dave is describing.

His phrasing is certainly humorous, but I don't believe it is either sardonic or sarcastic.

That specific sentence is neither.

The context of a statement is very important in determining if it is sardonic or sarcastic. This is especially so when the statement was written, as text does not carry vocal inflection very well and tonality is generally speaking, the most obvious clue.

Reading more of the essay than the question provides is necessary to answer the question. Thankfully, Lost in the Kitchen is not too difficult to find with a search engine.

Deciding the topic

According to English Grammar Today, a topic sentence is the first one in a paragraph, which should tell us sentence which tells us what a the subject of a paragraph is.

Introductory paragraphs are similar. As the name implies they are the first paragraph in an article, report or essay. Wheaton College states on their [Intro, Transitional, Concluding Paragraphs webpage](Intro, Transitional, Concluding Paragraphs ):

The Introductory paragraph introduces the paper's thesis to the reader. This type of paragraph is used not only to present the topic and organization of the paper but also to grab the reader's attention.

The second of those sentence is more stylistic advice, rather than a matter of grammatical necessity but it is a common sentiment. Capital Community College has a webpage, adapted from a handout by Harry Livermore of Cook High regarding five common methods to captivate the reader's attention including giving anecdotes and making a surprising statement.

Relevance to the Sentence

Let us re-examine the sentence with that in mind:

"But that, as far as I can tell, is not my point."

Dave's "point" seems to refers to the main subject of the essay:

21. Particular; single thing or subject. In what point do we differ? All points of controversy between the parties are adjusted. We say, in point of antiquity, in point of fact, in point of excellence. The letter in every point is admirable. The treaty is executed in every point.

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A definition of point from American Dictionary of the English Language (A.D.E.L.) by Noah Webster.

The intended subject of the report is clarified in the following sentence. "My point is that despite all that has been said in the past 20 years or so about sexual equality, most men make themselves as useful around in the kitchen as ill-trained Labrador retrievers."

My point is that despite all that has been said in the past 20 years or so about sexual equality, most men make themselves as useful around in the kitchen as ill-trained Labrador retrievers.

However, Dave has good reason to believe that we might think the subject of the article was supposed to be something else. Only one out of the three sentences in the introductory paragraph is related to the article's main subject, which is the topic sentence "Men are still basically scum when it comes to helping out in the kitchen."

The other two sentences in his introductory paragraph explain something else, his secondary insight made during the Thanksgiving Holiday, for a relatively long amount of time. If we got lost in the moment of his digression and forgot the topic sentence, we might expect him to continue discussing the reasons why Thanksgiving is not a very erotic day and subjects related to that topic. Even if it is not the main subject, as its placement in the introductory paragraph suggests, we might at the very least expect it to be relevant to the general topic but it really seems to be a non-sequitur.

While this digression allowed him to give a little anecdote and make a shocking statement that captivated his readership's interest, it has outlived its usefulness and he wants to get back onto the topic.

He is using the adverb not, to negate the substantive verb "is" to disassociate "that" from being the topic. This works because the word "that" can act as a substitute for just about any number of words, depending on the context:

4. that is also the representative of a sentence or part of a sentence, and often of a series of sentences. In this case, that is not strictly a pronoun, a word standing for a noun; but is, so to speak, a pro-sentence, the substitute for a sentence, to save the repetition of it.

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A definition of That from A.D.E.L.

Thus the antecedent of "that" is probably meant to be the digression in the two sentences prior. Dave's intent is just reminding us how thanksgiving is not erotic, or anything related to that, is not his main point. This allows him to segue into his intended topic, which is explaining how men are useless in the kitchen, with more picturesque metaphors.

Why His Intent Matters

The definition of the words you suggested to describe it rely entirely upon the intent of the message conveyed. The specific intent depends on which word is being used. In order to see how the words may or may not apply, we need to examine their meaning. Sarcasm is a sort of mean comedy:

Bitterly satirical; scornfully severe; taunting.

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The definition of Sarcastic from A.D.E.L.

Nothing about the message this sentence is meant to convey is either mean or funny. Next we should define Sardonic:

1. Apparently but not really proceeding from gaiety; forced: said of a laugh or smile.

2. Bitterly ironical; sarcastic; derisive and malignant; sneering: now the usual meaning.

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The definitions of Sardonic from The Century Dictionary and Cyclopedia (C.D.C.), 1911

The first of those is probably a more appropriate definition than the second. Also note that the American Heritage Dictionary 4th edition seems to have a stricter definition of sardonic, which is simply a synonym for sarcasm. Regardless for the sake of this answer, which claims that it is neither of these options, I'll assume the entirety of the C.D.C. definitions applies just to be safe.

Because sardonic can appropriately mean ironic and sarcasm is often confused with irony, as many statements are both ironic and sarcastic (See the American Heritage Dictionary 4th edition, which notes that sarcasm is merely "often ironic" rather than just "ironic" or "always ironic") the definition of irony is also relevant:

A mode of speech expressing a sense contrary to that which the speaker intends to convey; as, Nero was a very virtuous prince; Pope Hildebrand was remarkable for his meekness and humility. when irony is uttered, the dissimulation is generally apparent from the manner of speaking, as by a smile or an arch look, or perhaps by an affected gravity of countenance. irony in writing may also be detected by the manner of expression.

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The definition of Irony in A.D.E.L.

Considering that's antecedent, the sentence in question does not seem to contradict the message it intends to convey. "That", being why thanksgiving is not very erotic, is not the main subject of the article.

It is also not a sentence that is funny in isolation from the context, which is another count against it from being considered either sarcastic or ironic. The only way left that it could be considered sardonic is if it was a sort of falsified humor, cheer or pleasantry meant to politely spare feelings or evade scorn but no, the sentence in question is a mostly factual statement, with only very little if any emotion within it, so it is also not sardonic. Evading scorn especially seems to be the least of Dave's concerns.

The overall essay is very sarcastic and so is the sentence that follows but this one is not.

These are weird words because they're personal: they imply access to emotions and motives.
Nevertheless, they exist and we experience them, but getting the names straight is hard.
Etymology can help, sometimes. Both words come from French, but ultimately they are Greek.

Sarcasm and sarcastic come from the Greek sarx 'flesh'. They metaphorically refer to a beast shredding flesh with its claws and teeth. The implication is that sarcastic speech is not friendly and is intended to hurt. This is often disguised as humor, which the intended victim is expected to experience as not very humorous. Clearly, the subject of the motivations of speaker, addressees, referents, and bystanders becomes very complex very fast.

Sardonic, on the other hand, refers to the island of Sardinia, where Aristotle said the people had bitter and scornful laughter "apparently but not really proceeding from gaiety". Again, motivation and duplicity muddy the waters.

So it's not surprising that most people use them interchangeably, nor that there is no single understanding of their differences, if any.

What I do is reserve sarcastic to refer to obvious cases of aggressive language use, and use sardonic for those that are attempting to be funny without obvious ill feeling. But that's just me. Your mileage may vary; after all, it's your language.