Because MS see's Sony as a threat to windows and their software business. It's the whole reason MS launched the Xbox. In fact MS went to Sony and tried to get Windows on the ps2, but Sony said no.
Think about it. The Playstation 3 and 4 are multimedia boxes that don't run MS software. I use a Mac at work and my ps4 at home for all my entertainment needs. I am completely out of the MS software ecosystem. (And it's actually kinda nice TBH)
MS is desperately trying to get people back into their ecosystem, but other than the surface tablets it's not really working. Apple and Google dominate Tablets, and more importantly cell phones. Sony is now dominating video game consoles, and even amazon makes a TV stick that doesn't use MS software.
MS has been pushed out of the consumer software market. Which is why I think eventually they will pull an IBM and just focus on the business sector.
I think it's about MS's endeavor to make gaming a central aspect of PC gaming, that's been MS's focus back since Windows 95, you can see that goofy Bill Gates video where he's inside Doom and they talk about it. For trying to get console makers to use Microsoft's APIs I think had more to do with keeping games readily available on PC by sharing a lot of commonality with consoles with their APIs, they can help secure Window PC's advantage over Apples with gaming.
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