If I understand correctly, the phrase "x thinks it's people" is used to say that something (usually an animal) behaves like a human being. An example:
Wherever you turn your head, you can see a tabby in a party hat or a Siamese cat ‘playing chess like it thinks it’s people’.
From: Oxford Dictionaries Blog
But why do we have here "people" instead of "a human"? I mean, to me the structure of this expression looks like this: one entity (an animal) is many entities (people). Or maybe "people" is not a noun here?
Best Answer
This isn't a grammatical mistake, but a reference to an old Simpsons episode from 1994. The phrase is meant to be said in a condescending tone: "Aww, it thinks it's people!" It means exactly what you think it means. The grammatical error is done intentionally for comedic effect.