The custom NXT to MIDI board is the key to making it work.
The board is supplied with power via Port A, with enough juice to power an external speaker. Piggybacking on the board is a VS1103 MIDI synthesizer and a Teensy controller which converts the NXT signals into MIDI commands.
On the NXT side of things, there are 3 touch sensors and two motors (for the rotation sensors). Three touch sensors gives you 7 possible combinations which works well for the notes in a scale. The top rotation sensor controls the volume and the bottom rotation sensor controls the octave. From the video it looks like there are 3 octaves of notes available.
What makes it really cool, is that MIDI means you can create all types of different sounds, from pianos to trumpets to pipe organs :) Press the on-board NXT buttons changes the instrument and from the software it looks like there are 128 instruments available.
Lots more information, including full schematics, code and everything else you can think of here.