Thank you, stan. I meant Steam on Wine and not actual Windows, but you figured it out.

Well, here's a bit of extra info. I've found that you can login to two devices at the same time with the same Steam account, but it will only let you play a game on one device at once.

So for instance, you could login to Steam on Windows on machine 1, and Steam on Linux on machine 2.

Then you could use Steam-Link Streaming to play a Windows game on Linux, or vice versa. I'm actually thinking to do that very thing. Launch Steam on a different PC running Windows, and then play a Windows-only game on Linux via streaming. (Plus there are other ways to do this without running Steam twice, if so inclined.)

So you can only download Linux games using the Linux client of Steam... while I can choose whatever platform I like using GOG.com and the lgogdownloader package?

Yeah, another reason to avoid Steam I guess.