You can still use WebStorage for a desktop game. Sounds a bit counter-intuitive, but all Awesomium does is basically launch a new self-contained Chrome, meaning it still has the bells and whistles of a browser (probably not all of them, actually, but definitely WebStorage).
There was a glitch when it was first implemented that wiped all the data you stored when you closed the game, but I'm preeetty sure that was fixed. Someone correct me if I'm feeding this poor man lies!
EDIT: Ninja'd! SullyTheStrange2012-09-12 21:47:41