I like the idea you have here. However, the curser lags a bit. I like how each tile is pare of scene from an anime, however I find it a bit disorientating. But then that's just because I'm a thick westerner. With the controls, could you reprogram them, so you just click on a tile, and it lights up or glows or something, or pulses and when you click on another tile, they both swap positions. The current control scheme seems a little over complicated to me.
Another feature you could have is when a piece is in the correct position or place, it could be locked there and this could be signified by making it's alpha 100% or something.
Also I like how the scene is taken from an anime (from the 1990's I'm assuming form the picture quality and everything. I remember that style). I'm interested in watching the anime this was taken from, can I ask what the anime is called please? Thanks. Either leave a comment on here or you can message me privately through this site.
Over all I like what you have here, it needs some readjustments (mostly controls), but no one get's it all right on the first go. I have met designers in industry who keep making mistakes but learn from them. I can see you wanted to have some interesting controls here, but it just makes things a little to complex (for me at least).
But as I keep saying well done, this is quite a polished product.