"And that's it now you can move your hand above Flick board and if everything is correct music will be played"
Uhh, what kind of Music? Author could have given at least some description of how it works or how it sounds... Like a Theremin, perhaps? A quantized Theramin, which steps through precisely tunes notes in a chromatic scale? What is it?
You are right. I should write question "How this Instrument could be classified.."
Looks like Theremin, but it is like MIDI synthesis programmed in Arduino. Eight discrete notes along X axis, and two different shapes sine and triangle change along Y axis. Note duration change with height above board.