If you have Game Pass, would you use its cloud gaming service, or would you go out of your way and play in Luna, which by the way, does not have as many games?
Also, Amazon does not have the software platform, nor the hardware, to compete with Microsoft (Windows, Xbox).
Microsoft could and does bundle a Xbox app in Windows, which also features their cloud platform very prominently [0].
Essentially, every single Windows user is being introduced to Microsoft's very own cloud platform. It's not that Microsoft is "treated differently", they are indeed different.
I have both prime and game pass ultimate and use neither bc honestly cloud gaming sucks, even with google fiber.
But you have. Inadvertently, but you did.
I think you don't understand Microsoft's idea of vertically integrating your gaming experience, and it isn't even a new concept for them, as they have been doing it with pretty much every single market they have got into, e.g. Office, Internet Explorer.
Microsoft bundled cloud gaming inside their subscription, because that's how they target users who want to play games. Same goes to the fact that they very prominently provide access to their cloud gaming service from their two gaming platforms, Xbox and Windows.
It is fair to say that people with a cloud gaming subscription from Microsoft are, in fact, gamers.
In comparison, Amazon bundles several services in Prime. I didn't even know I had free access to some Luna games. The other day I found out that I could stream some free music as well. I don't agree with their model either, but I bet that the vast majority of Prime members aren't paying Amazon just to have free access to Luna.