Yes, "The Knight's Tale" is set in Athens and Thebes, but don't forget that it's Athens and Thebes from a medieval English point of view. This isn't like reading Sophocles's plays. That's why so many of the things the Greeks do look an awful lot like stuff medieval English people might do, like fighting in jousts, engaging in courtly love, and practicing chivalry. So how is the setting impact the tale, if at all? Why not just set the tale in England?
Well, for one thing, a lot of the philosophizing that Theseus does comes from ancient Greek philosophers. When he talks about God creating beings in a "faire cheyne of love" (2130), he's drawing directly on an idea from ancient Greek philosopher Plato. When Theseus talks about how it's best to accept whatever life throws at us (like Arcite's death) without too much angst, he's drawing on an ancient Greek philosophy called Stoicism.
Another way in which the setting colors "The Knight's Tale" is in the appearance of Greek gods – Venus, Mars, and Diana. (Actually, those are their Roman names. Their Greek names are Aphrodite, Ares, and Artemis, respectively. But same idea.) The tale has a scene in which Mars and Venus argue about whose knight will win. This kind of scene could come straight from an ancient Greek epic like the Iliad. It illustrates a point of view that powerful forces outside of human control are at work causing everything that happens in the world.
The ancient Greek epic point of view might say that these powerful forces are the all-too-human seeming gods. The ancient Greeks might say that your death could be caused by nothing more than Mars's squabble with the god you made the mistake of praying to the other day.
In contrast to this, Theseus chooses to see an event like a death as evidence of an orderly God who has an orderly plan for the world. This is a more medieval Christian point of view. What we see in "The Knight's Tale," then, is an ancient Greek setting and worldview rubbing up against the medieval Christian point of view of its teller.