So, I don't understand what's happening at the start of this level where you drop off the edge, turn around, and warp to (I assume?) a later checkpoint. I've tried it a bunch of times but it doesn't work for me.

Also, is this really not a glitch? Cause it seems pretty glitchy.

I believe how it works is that to the left side of where you start off there's a checkpoint that tells the teleporter to put you back there when you fall down, but for some reason the default checkpoint on that level is further into the level so if you just avoid the start checkpoint you will get there when you fall down. You should get it every time if you just walk forward without moving your mouse.