I think that the circuit at the top center of the chip detects collisions. E.g. if the paddle is being drawn at the same screen position as the ball, then you know that the paddle has hit the ball. This way, you don't need to store the paddle position and you don't need to compare the paddle and ball positions, you just check if a paddle pixel and a ball pixel happen at the same time.

I haven't figured out how the ball position is stored. It seems like they'd need a register for the X and Y position, along with an incrementer/decrementer, but I couldn't find that. Maybe there's something tricky going on. Or maybe I haven't looked in the right place.