Like the other reviewers, I like the concept. Like the other reviewers, I find the game a bit slow, and this is even with the inclusion of the speed up. Level 8 was annoyingly slow, even using the spacebar.
That aside, this doesn't feel particularly skillful to me. Skill to me implies that I have a certain level of control in the game, and this game doesn't have that feel to me. Maybe it's just the speed of rotation or the narrowness of the corridors, but most of the time it just felt like me getting through a "doorway" was more luck than skill.
And that's my real problem with this game. Moving up a circle feels damn near impossible to accomplish a lot of the time. Level 8 was a total gamebreaker for me. Trying to go left by the orange door was a nightmare. It felt like no matter how early I entered the "door", the circle would get clipped trying to go through.
I guess overall, it didn't feel either very puzzling or really skill-challenging. It was more frustrating than anything. Knowing how to complete a level and being unable to do so is bad enough, but when the player feels it isn't their fault it's even worse.
To rip a whole paragraph from JonTron, you get points for the attempt, and this certainly isn't the worst game I've ever played. Hell, I honestly can't even call this bad, it feels more like it's unfinished. I'd call this the "alpha" stage of the game. With some polish I think this could be a very cool puzzle game that provides a good experience.
But as it stands now, I can't really call this a perfect game, a great game, or even really a good game. It really feels incomplete. Try expanding the corridors and doorways a bit, maybe create a few alternate speed buttons (slightly faster, fast, fastest) to get around the issue of speed. I muted the music immediately, so I can't comment on that.
Overall, this looks like it could be heading in the right direction. I honestly hate leaving this rating, because I feel like this could have been pretty fun with a bit more adjustments. Don't give up on it, play around with it for a bit and get some more tweaks in there, and you just might have yourself a 4 star puzzle game.