I don’t think there’s a way of checking how many games are like this, but I find that the majority of games I’ve tried doing that just work, and the ones that don’t are mostly bad programming (e.g. crashes trying to load the steam library).
That’s GOG’s whole schtick, none of the games they sell have DRM when purchased from their store. You can always copy the installer to another computer and run it.
That’s not entirely true, as a general rule I think GoG has a lot less DRM-ed games, but it’s not 100% DRM free like they sometimes claim https://www.gog.com/forum/general/drm_on_gog_list_of_singleplayer_games_with_drm/page1
As much as I disagree with your last statement (I think Linux for client is on par with Windows for the vast majority of users), I strongly agree with everything else. This wasn’t a Windows problem, but a “your IT is cockblocking you” problem, it could have happened in Linux too if it wasn’t because he used a rogue device, he could have fixed it on Windows too doing the same.
Personally I would have gone straight to Linux because I’m out of the loop on how to do these sort of stuff on Windows. If it had to be Windows, let IT figure that out, their firewall, their anti-virus, their problem.