The way things tend to work is that owning something on one store doesn't mean you get it for free another store, unfortunately. With some exceptions. For example, if you contact the publisher and explain your problem, they could be willing to offer a key to redeem the game on another store if there's reason to believe that doing so would fix your problem. It shouldn't hurt to ask (and I've certainly been granted such a key in the past), but I wouldn't hold my breath.
You could of course ask GOG too but I don't think it'll work out. I mean why would they shoulder the cost and provide a free service to make up for other stores' failures? Speaking of which, have you contacted customer support at Windows Store?
