Was this subject complement diagrammed correctly?

I believe the author is right. "Time" is just an object in the adjective phrase "time consuming", which is built on the model "verb and object"; you can say "feeding is consuming time".
It wouldn't be correct to say "feeding is consuming" as something would be felt to be missing (time, energy, supplies, …), yet it would make some sense; however, "feeding is time" can't make any sense except in a very elliptical manner as in "Time is money" (of course, speaking literally, "time" is not "money").
According to this understanding "time" is accessory in the syntax; therefore, it is made to depend on the branch rather than constituting it.

I love this question. It points out an interesting aspect of how the present participle forms phrases versus how the present progressive tense operates--and the difference in meaning.

But, first to answer your question. Simplifying the example to, "Feeding goats is time consuming," makes clear that "is" acts as a linking verb. So, "time consuming" must be a subject complement, which means that it must be in the nature of an adjective or a noun. "Time consuming" definitely is not a noun. To prove it, try to use it as the subject of a simple sentence. It won't make sense. It must be an adjective. Since it must be an adjective, its head should be an adjective. Between "time" and "consuming", "consuming" is a present participle which acts like an adjective, and "time" is not an adjective. So, "consuming" must be at the head, and "time" must be complementing it or modifying it. Since, "time" is a noun, it doesn't really modify other words, so it cannot be a modifier. It must be acting as a complement. In this case, it is a complement (or direct object) of the present participle, "consuming."

The cool things, here, is that "time" can go before or after "consuming." "Feeding goats is time consuming," and "Feeding goats is consuming time," both work. The former is constructed with the present participle, and suggests that the act of feeding goats takes a lot of time. The latter uses the present progressive, "is consuming," and suggests that a specific and currently happening event of a feeding goats is using time.

I would argue that the particular construct of your example is almost idiomatic in nature. Normally, "time" as a complement of the present participle would follow the present participle. Here, "time" precedes the present participle because, otherwise, the sentence would have an entirely different meaning. Inserting "time" between "is" and "consuming" prevents inadvertent formation of the present progressive verb. But, it also makes for some confusing syntax for purposes of diagramming.