I would be very dubious about buying the above. The photo is one that turns up on a a mere half-a-dozen obscure sellers, a couple of which include reviews stating that the receiver is a third-party knock off. The sellers are all in Japan, none are official or have much in the way of 'history', i.e. a large number of positive reviews (not that that's always a guarantee). In short, the above will (like all I've seen) be a cheap copy that may or may not work.
Microsoft no longer sell the official receiver as a standalone product. I don't know why, but they don't, and that's probably why nobody else does either. The only way to get hold of one is to buy a
wireless controller for Windows or find somebody selling one secondhand.