Why do you keep talking about it as if it's just a theory?
The CEO has explicitly stated he thinks only about 3 products (Azure, Windows, and Office), with everything else being parts of those pillars, and Xbox, its first-party studios and Xbox Live service, will be used to drive Windows across PC, console, mobile, and HoloLens.
I suppose you can say Xbox was demoted in the re-org if that's important to you to see it like that. One could also say the Xbox division is better off being one of the main parts of the Windows strategy when the new CEO re-aligned every part of the business behind his mobile-first vision. Perspective. No harm in leaving you to yours.
Their intentions to move out of the dedicated console hardware market has also been made crystal clear. A dedicated console doesn't fit anywhere within the CEO's agenda no matter how you spin it. Gaming for a OS does fit in his strategy, because he explicitly said so. With what Spencer has said thus far, they'll obviously be some type of Windows 10 machine more akin to a PC, perhaps in small form.
Long term? I suppose the Xbox team will make games wherever they see the most traction in the Windows Store. Ultimately that could be PC, tablet/laptop, phone, HoloLens, or something else they haven't made yet. It could also include a device for the TV for all time to come. We'll see.