As the question implies, if you swallow part of an animal do you think it mean it can be can be considered "swallowing an animal"? My argument was that part of an animal doesn't mean the whole animal.
Here is the link
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As framed in your question and link, an animal refers literally to the whole animal (or at least its edible portions). Eating a horse means consuming the whole horse, not just a small bite of it, hence the force of the idiom I'm so hungry I could eat a horse.
However, the puzzle posed in your link doesn't require the whole animal (or more generally, the whole object):
If you swallow me, you'll live, but if I swallow you, you'll die.
In this case, it's possible for your assertion in this ELU question to be both grammatical and correct, but you'd need to replace an animal with the uncountable form. It would be treated as food in one place, and an eater in the other.
Is it acceptable to use the word in different senses to replace the first person "me" and "I"? In the context of puzzles, this may be acceptable.
[As an aside: note that even the accepted answer (water) relies on this idea to some extent. The quantity of the water that is swallowed (at least, in a single sitting) is significantly different from the quantity of the water that swallows.]