I was wondering if menus have to only use one button, or if the rule only applies to the gameplay.

Last I heard it was just the gameplay but am guessing the judges would be impressed if teh menu was also one button?

To my mind, you must be able to start, play, and restart a game using a single switch, at the very least.

I agree with OneSwitch. After all, if you can't even start the game yourself, it defeats the premise.