Interesting game. I can't say I liked it that much, but that was mostly because the controls were a bit awkward. I feel like you could make a game where the ways that you die allow you to unlock new abilities quite well. The level felt a little cluttered as well.
Also, a point of feedback, try not neglecting sound in a game. I think a single looping music track would have made the repetitive gameplay easier to get through.
I did beat the entire game, though. It felt significantly better to play once I unlocked the double jump. Definitely a good start on this mechanic, and I think you could definitely do it better!