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.
The brilliance of this is there's no chance of bugs caused by the internal paddle position (that causes the ball to bounce) not matching the drawn position, which would make the ball either pass through the paddle or bounce off nothing. Whether that was any part of a motivation for this design or it was purely driven by technical limitations, it's just a very elegant solution.
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.