This reminds me of an old flash game called Continuity but in that game the map was a sliding block puzzle and the map segments had to strictly line up terrain-wise. This game gives a lot more freedom in that the pieces don't have to strictly line up which is nice. I really liked how mechanics were slowly introduced and also alluded to. The enemy walking around the wrap around was especially noteworthy (he even conveniently dies on a spike afterwards). Overall the game had a nice polished feel with a good fleshed out mechanic.
I did run into a bug on level 14 where I jumped down the piece leading downward and went through the roof of the piece below—effectively putting me back at start.