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A flute normally has about 2 octaves of diatonic notes, certainly true for a recorder. I'd suggest expanding the number of usable notes so that some could be used for compound commands.
In saying that, what would be even better, would be to allow the use multiple notes at ones, polyphonic instruments, so that chords could be used for this effect. Say you play a C to walk forwards, a G to strafe right, and E to shoot, then a C major triad could be played to do all these things simultaneously. A flute quartet could maybe play the game together.
Top comment there is: "The Pied Sniper" (!)
That clip appears to be from https://www.twitch.tv/deanobeano/clip/CharmingDoubtfulCattle... (note: brief profanity at the end of the clip).