clarry: Just remember, the DRM free part doesn't apply to multiplayer.. so yes it's quite possible for your game to become unplayable if GOG or the games' DRM servers go down.
It's true that if the game's matchmaking service or servers get shut down that the game may no longer have matchmaking abilities built into it at least, but worth noting that many (but not all) games also have direct IP and/or LAN and/or local multiplayer which is not dependent on 3rd party centralized servers. Also worth note is that a number of games in GOG's catalogue that originally had multiplayer when they first came out years ago either never came with multiplayer from the start on GOG (such as the Full Spectrum Warrior games), or the multiplayer matchmaking died when Gamespy or other similar services died. That's one of the unfortunate things about multiplayer matchmaking services, is that they are centralized by the very concept of their designs. While GOG Galaxy multiplayer is now a new option for some games that choose to use it, and it's arguably a better option that games using 3rd party services such as Gamespy or similar because GOG Galaxy multiplayer should theoretically always work as long as GOG exists, should GOG cease to exist then the matchmaking provided by Galaxy may no longer be functional as well. Hopefully more game companies will recognize the value of retaining or adding LAN and/or direct IP multiplayer to their games as was standard 10-20 years ago. IIUC, Divinity Original Sin does this so some companies still care. :)
HunchBluntley: I do apologize if I overstepped. My "TL;DR" post was partly joking, and I didn't mean to piss off one of the more genuinely helpful forumgoers. I also don't want to derail this thread any more, so I'll leave off.
I'm not pissed off for the record. :)