YouTuber conquerearth explains how it works:
The sound from the theremin is split into its frequency and amplitude components in real time, which are then mapped to values in a linear scale representing the X and Y axis. Pitch becomes horizontal control, and Volume becomes vertical control.
The X and Y scales are then cut up into different zones. In this case, Left; Right and dead zones for the horizontal, and a single trigger and dead zone for the vertical.
The trigger zones are then mapped onto a virtual joystick hooked into an emulator.
The end result is a fairly usable input control for playing games like mario. The bars give the much needed visual feedback as to how "in tune" you are, so you have a better feel of where the trigger points are.
As conquerearth points out, it's possible to control the game with your voice or even a guitar or a violin.