I have a bunch of original MS ones and they all work perfectly fine with 8.1. No drivers needed.
Are you sure your adapter just isn't broken? Or maybe it's one of the knock-off models which requires you to manually install the drivers.
Worth checking out if it is already dead imo.Cool, I got one as well.
Protip: You might need to do this one day when the fuse blows: Wireless receiver fix