I thought this game was genius. I've been trying to do a 6DOF dungeon crawler forever and you nailed it.
It's on par with Portal as a puzzle game imo, but this is kind of the Narbacular Drop phase.
My main critiques are that I found the camera disorienting at first, I think it'd be nicer if it was centered on a point when rotating rather than being on an arm. Once I stopped using the mouse though I was fine with it, I had a better time with the keyboard anyways. Maybe adding a keyboard button to fire would be good too so the user can forgo the mouse altogether.
I also found the collision of where I could and could not rotate/walk to be rather opaque at times. Particularly the metal didn't seem intuitive that it was unwalkable, I think they had this same issue in Portal which is why they made the contrast between metal and concrete basically black and white. I also found the grey edge pieces didn't always connect every wall I could walk on, sometimes there'd be none and I could still go up it. This was exacerbated once the moving cubes were added as I couldn't tell what edges I could walk on, it seemed like maybe only the surfaces with the arrows could be.
I thought the floor lights/glowing cubes were lava at first so I avoided them for awhile.
Levels 8 and 11 filtered me, but it was alright because you allowed alternate levels to let you progress. Really good idea there.
I had a really comfy time with this, I think it's the best I've played so far this DD and I can't wait to see more mechanics and levels. I think you have a really good one on your hands.
It would be interesting to see if shooting an arrow straight above you could unlock even more puzzle designs; really take advantage of the 6DOF.