For macOS you're probably right; a Vulkan rewrite is likely not worth the expenditure.
> Firstly, what do you mean by competitors? I'm pretty sure none of xCloud, Playstation Now, or Nvidia Now use Linux systems.
I see no reason why Nvidia wouldn't use Linux where possible. Windows, especially cloud based Windows, has weird and sometimes expensive license charges that any Linux-compatible game does not need. They're likely still going to run Windows VMs out of necessity, though. I don't know the game streaming market well but with the groundwork Valve laid down for SteamOS support, I can see Stadia competitors choosing to use Linux as a cost-saving measurement. Still Google is quite some party to ignore.
Aside from dropping generic Linux support (which, of course, has an infinite amount of configuration options, especially when you encounter Arch and Gentoo users) they're also dropping SteamOS support. SteamOS (Debian with a layer of Valve software) deals with basically all issues you might have with libraries and versions for you.
This sounds like a choice based on economics (cost of testing Linux packaging vs income from Linux users) but if I were a Steam box user, I'd want the money I've invested into the game back. Based on the laws in my country, I'd say the product will be mostly broken (the main component, online play, will be intentionally disabled) which might be reason to terminate the purchase agreement (i.e. trade the product back for money as its manufacturer will not fix the shortcomings introduced). They'll likely fight tooth and nail to prevent this but one big lawsuit and the cost of maintaining limited Linux support would likely outweigh the cost of killing it after selling the game with Linux compatibility.