I'm a Linux user who buys a lot of games on GOG and I've never had a problem running them using Wine stable, with the only exception being games that supposedly don't even work on Proton yet.

Majority of the games there don't even come in a native Linux form, and those that do can be a hit or miss when it comes to compatibility - at least one game I tried needed a dependency from a no longer available package. Alternatively a few titles come shipped with some kind of wrapper that's really just an outdated version of Wine surrounding a win32 EXE.

Also, isn't the point of buying something DRM free that you don't have to use a client or any other online feature? The offline installer has always been GOG's killer feature in my book, that's how you make sure the game gets truly preserved.