I finally figured out an in-continuity reason why the Burly Brawl looks like a crappy video game for its second half! It is a crappy video game! The rendering engine for the Matrix itself can’t keep up with that many polygons moving that fast at a lifelike framerate, so everybody’s faces and clothing lose polygonal depth and end up looking smooth and unrealistic.
I only regret that this does not explain the increasingly monologue-driven and stupid plot. (To see me regrettably attempting to do just that, please reference The Grand All-Encompassing Star Wars Conspiracy Theory.)