Should I use a colon after 'as'?

You have a number of options at your disposal. Here's an interesting one that--while wordy--might be appropriate in an introduction to a paragraph or two on the topic of totalitarianism:

The main subject of Animal Farm is totalitarianism, which is defined as a system of government that is a) centralized; b) dictatorial; and c) demanding, by requiring complete subservience to the state.

But no, you do not need a colon after the word as.

Punctuation is somewhat subjective. However, one could see how a colon only slows down the reader here.

Common colon mistakes

Using a colon after “such as,” “including,” “especially,” and similar phrases. This violates the rule that the material preceding the colon must be a complete thought. Look, for example, at the following sentence:

Example (incorrect): There are many different types of paper, including: college ruled, wide ruled, and plain copy paper.

You can see that “There are many different types of paper, including” is not a complete sentence. The colon should simply be removed.

— University of North Carolina

Animal Farm is a book title, and, as it currently stands, it should be in italics:

A couple of generations ago, it was the custom to enclose all titles in quotation marks: titles of books, titles of poems, titles of films, titles of newspapers, and so on. This usage, however, has now largely disappeared, and the modern custom is to write most titles in italics.

— University of Sussex

When stating the definition verbatim, use quotes. Using them otherwise might show skepticism³, so I would recommend dropping them. I think this definition is verbatim.