GD is a platformer. Not a rhythm game. If you think this proves anything, then it’s a pretty bad attempt at doing so. You can sync as many clicks as you want, or even use different keys, but your clicks are many times not syncing to the song as much as an actual rhythm game would (also the random parts in between where you don’t click anything but there’s stuff going on in the song), because you’re adapting a platformer to have jumps to the song, also note that you can’t play the game this way without external modifications. With this logic I could call Super Mario World a rhythm game if I hold right and make a hack with levels that have jumps and inputs that sync to the background music. You can simulate a rhythm game experience in GD, but you can’t call GD itself a rhythm game, because fundamentally it is not.
GD is a borderline rhythm game, but in this you always have to FC a level to beat it. I would say GD is a perfect balance between a platformer and a rhythm game.