Sorry, my bad. It actually was the mixer. Apparently the game itself is not very loud and the mixer actually was set on a low volume. I must have forgotten about it after adjusting it in the past. This combined with the low volume on my headset resulted in the sound not being audible at all.
I'm glad I still got to play this game on time, since it's really fun :) The difficulty is quite high, but I can do alright on the some_piano level.