Maybe Amazon aren't interested in the Xbox one but instead looking to buy xbox 360 assets and intellectual rights at a knock down price. Microsoft may be looking to abandon the 360 soon to concentrate on xbox one.
Amazon could then release a set top gaming box based around the 360 around £100/$130. They could enhance it with a high speed mode, more memory (2GB) and a higher quality upscaler so it can run both existing and a new generation of games that perform between 360/PS3/wii u and PC/Xbone/PS4. Removing the optical drive could save money and it could run android apps etc under arm emulation on the PPC chipset or a smaller supporting arm processor. That way the box could feature enhanced 360, original 360, original xbox, kindle, android and lots of media compatibility. Games could be demoed, rented or owned (like steam).
Microsoft will be abandoning the 360 soon and such a box wouldn't be direct competition to xbox one as it would be lower performance. Also Amazon could do a firmware update for existing 360 owners that added much of the functionality of Amazon's new box to existing 360 models if users accepted it. They would still have use of their 360 game discs. Microsoft live would be replaced on 360 with some new Amazon service possibly free but that would push movies, music etc more. This would also help motivate 360 owners to migrate to xbox one.
Whatever I think Microsoft have a huge battle on their hands with ps4 and the future looks like Microsoft will struggle to compete with ps4 unless they undercut it on price. I wouldn't ever consider buying a Xbox one at anywhere near ps4 money and currently its more expensive so as you can imagine a xbox one isn't on my shopping list for the foreseeable future.
