The movement is quite as tight as this kind of game would require, but the idea is super cool and the level design is quite engaging, I would love to play more if the controls felt better.
Also I know this is highly personal opinion but I don't think chugging metal guitars fit well to the game's visual. You could still do some high energy soundtrack, maybe using a synth's arpeggiator instead or having rhytmic stabs/comping from an electric keyboard like a Clavinet.
I did have fun and would love to see what else you can come up with!