The movement is slick and responsive, and the music is a good choice (even if you didn't make it).
The stylish lack of visual flair, and the little trail your avatar makes are both excellent touches.
I don't think the game needs a tutorial, but it would benefit from pieces that are more intuitive to interact with.
The white squares, for example, are totally opaque until you understand why they kill you. You might want to have them change how they look if you're in the air.
Overall, it's a solid game, and I had fun reviewing it.