Okay. I took some time, had some "fun", and rouuuuughly figured out how this works. Approximately.
The entire game is built around a PNG, that contains all possible board setups for Tower of Hanoi. When you click a button, it... essentially scrolls the PNG around. And as a result of that PNG's position, the rings get displayed, as.. I think different images embedded in the code. I didn't actually get that far, I just needed to know broadly how it worked.
Anyways my head hurts but I figured it out so that's enough activity for today.

