To the best of my knowledge there is still no proof that Valve plan to use Xi3 for their own steam box, it is far more likely Xi3 are one of the many partners that Vavle are talking with to make Steam compatible devices. From what I have been reading Valve plan to design their own Steam box but are also allowing 3rd parties to design and distribute their own with a variety of hardware levels and price points. This article makes a lot of that more clear:

So we really have no idea what they have in store harware wise for their own Steam box, other than what Gabe has alluded to with the fact that the "better" level they plan to focus on will have dedicated CPU and GPU, meaning an AMD APU is likely not even on the table for the official Valve Steam box. Nvidia seems to have a better working relationship with Valve and have the best driver options to date on Linux, my money would be on Valve going with Nvidia and the proprietary blob.