If you can "read" a schematic, you'll see that it's actually fairly simple; in fact, you should be able to notice the repetition of many areas - it's a very modular design.
Just a bunch of simple and repeated circuits arranged in a certain manner; it's essentially a very special-purpose "computer" where the "code" is fixed in the hardware (literally "hard coded"). Much of it borrows or is identical to analog computing circuits (most especially the way the "ball" is drawn - sine/cosine waves generated and scaled, then combined on the x/y axis, which are also updated by oscillators for the ball movement).
Don't get me wrong, it's an amazing achievement, especially done "blind" and "dead-bug" style.
Also, note the various places where it looks like two diodes are in parallel, hooking up one line to ground. I'm not sure exactly what it is doing here in this circuit, but I know that in single-element ultrasonic distance sensor circuits, such a similar construct is used to protect the input of the receiver portion of the circuit from the high-voltage (due to amplification) of the transmitter when the "ping" is generated; in other words, it acts like a "voltage clamp" or filter to attenuate the signal. That is probably what is going on here, too - to prevent high-voltage spikes from being transmitted further down the line, and routing them to ground. Something like that...
Moving the bars with knobs, and drawing lines is fine, but doing bounce ball effects with sound.. miracle