This is kind of an odd question, because it presumes a very silly model of gravity. People who had any kind of understanding of a spherical Earth understood that they might not be at the absolute top of it. Thus any notion of gravity (however folk) had to take into account of the fact that you don't fall over sideways being closer to the equator.

Separately, just because their understandings of gravity were, to our eyes, wrong, does not mean they were wrong in that way. Aristotle's theory of why things traveled towards the "ground" is that they were in fact traveling towards the center of the universe, as this was their natural place to be, and everything tends towards its natural place. This would hold no matter where you were on the planet, because in his view the planet was the center of everything.

Something I like to point out whenever people marvel at the inadequacies of other theories of gravitation: Newton's theory of gravity is not, by our modern Einsteinian understandings, completely correct either, but it manages to explain quite a lot within certain limits of experience. Even the Einsteinian understanding is known to be incomplete within certain ranges of experience. So "our" understanding of gravity is clearly not necessary for this kind of query, and we should keep in mind that most people today (even my very bright, engineering-school students) tend to forget that we do not in fact live in a Newtonian universe, and may not even live in a purely Einsteinian one, in the end.