Seems to be a problem with the underlying Wine setup, but I can't find any configuration that changes this. I have similar results in both Wineskin and Crossover, so it's some sort of universal incompatibility between the two now. The game runs at about 1FPS and is unusably slow, Battle.net essentially crashes the app with a white screen and everything rendered on top of each other. It's a shame because it used to work incredibly well.
Demo: http://vid.ly/4a6y0v