Well it seems like an interesting concept and I was definitely interested in seeing where it went considering the setup on the page. Unfortunately though as you've said below you ended up just going with a basic twin stick shooter, which is alright.
My main problem is with your "chaos" element of turning the screen. There's literally no indication of what is happening, when it will happen or how to deal with it. Which obviously leads to a bit of confusion, mainly for me and a few other people that was in the form of thinking it was teleporting.
Otherwise though, it also completely messes up any orientation in terms of maneuvering around the map, especially since there is no larger map to use to orient yourself around. Or any major landmarks to remember and base your path off of. That's obviously assuming there is actually somewhere you want to go, which there isn't much indication on where that would be either.
So overall, a nice base system and a decent tileset for a map, but I definitely feel like the overall design should be a little clearer. At least something indicating the screen is rotating, or when, along with some better landmarks to orient yourself around I'd say.