When the 555 fires, it brings VPAD1 low, and a counter starts counting horizontal lines. When it reaches 15 (starting from 0), it brings VPAD1 high again. So, a paddle is 15 vertical lines high.
A second potentiometer, "Paddle 1 Control" is used to calibrate the circuit so that the paddle's position ranges from the top to the bottom of the screen. The original game had a bug where the paddle wouldn't go to the top of the screen, but there seems to be no issue with that here. Perhaps the trim pot isn't set correctly, or else there the simulation isn't accurate enough to reproduce the bug.
Next: Drawing the Paddles.