So, I don't care whether a game is native [1] or run on an emulation layer as long as it works and performs reasonably well and, most importantly, it is supported.
[1] the reality of course is that many, but not all, native ports still run on some sort of buggy, proprietary translation layer.
So Valve tried to break the Windows monopoly on games by creating a native Linux SDK and releasing the Steam Machine, which was based on Ubuntu. The goal was to make Linux a first class citizen as a gaming development platform, not just something to run an emulation layer. The Steam Machine failed, because it simply wasn't very good. Valve quickly lost interest in native Linux and let the native SDK rot away into obsoletion. Fortunately, Microsoft being Microsoft, the Windows Store was (and still is) a terrible platform, so pretty much nobody is buying games there (except for Minecraft), and you can still install anything you want on Windows.
So of course you can say that you don't care if it runs natively or in an emulation shim. It would have been nice if Linux had become a game development platform and not just a kernel with a Windows API layer on top. So in a way, Linux' success here is similar to Android's: Yes, it's technically Linux, but not really.
Microsoft has the disadvantage of being the biggest platform and the most scrutinized.
The Microsoft store is as good as the Apple and Android stores, but people using Microsoft are much more used to downloading something from the website they want to install something from. And developers don't have a strong incentive to send them to the Microsoft store from their website.
And Microsoft being such a big player, even time they make moves, everyone else digs in to prevent them from taking over. An example of the is steam machine.
Was it? Or was it a strategy they ended up not needing?
Your recollection is incomplete. Microsoft was threatening to lockdown Windows app installations by requiring app signing for all executables in Win10. In the worst case, it meant the Microsoft Store would be the only store on Windows, and Steam simply wouldn't work on Windows.
Microsoft was toying with an idea that posed an existential threat to Valve. IMO, Valve's goal was to be unshackled from Microsoft's mercurial whims, and despite a slow start, they have finally achieved that goal in the last few years. Microsoft is still proceeding doen the TPM path, and has a turnkey walled garden - I think Valves call was the right one.
https://github.com/ValveSoftware/steam-runtime#default-tools
Have platform agnostic code, or let it prefer windows. If your compatibility layer is so good I don't care.
Better than what we have now where tons of applications don't run on Linux or Mac OS.
So they care so little about Linux they are going to release a subsidized console using Linux next year? Give me a break with your cynicism.