When on Linux running the itch.io client on my library show Windows-only games...
Why?
Being on a platform and look for stuff form another one (assuming you have that platform at all: not all Linux user use Windows) is the exception, it shouldn't be assumed as normality.
"you may be interested in something currently unavailable to you" doesn't sound a reasonable paradigm.
Would be this convenient also for Windows user with Linux's only games? Probably a OS they didn't even consider?
Yes, because you don't know why they're looking for games for another platform. Maybe it's for a friend. Maybe they're browsing for a mobile game, but from their desktop where it's more comfortable. You just don't know. So the app rightly shows you everything by default. Feel free to apply all the filters you want manually.
I'll skip the fancy things and narrative examples: I do strongly suggest to check how other well estabilished stores behave with their app/launcher into prioritize actual and real information the customers is actively providing.
If they are on Linux, they did install your app on Linux. They are giving an empirical and factual proof they are on Linux client.
As well as
If they are on [otherOS/device] they did install your app on their [otherOS/device]. They are giving an empirical and factual proof they are on [otherOS/device] client.