I have found this:
https://www.gog.com/forum/general/star_wars_battlefront_ii_now_supports_crossplay_e3898/post93 That explains why I didn't get a changelog and didn't download anything, so the old multi-player is still available and Galaxy is indeed optional in this case. :)
I will add it do both lists then.
Does it have LAN support?

Ah I see well I am not sure but people was bitching in the comments so I would dig through everything, I have yet to re download the new version or something but I hope it does...

Added Worms W.M.D
to the Galaxy dependent MP games.
Well, there goes my interest, I'll have to keep playing Worms Armageddon online via Linux then...

I see that Stronghold Crusader (Extreme) is in the LAN-only list, which is correct (love this old game). Unfortunately, Stronghold Crusader 2 does not support LAN multiplayer, requiring all players to be signed into different accounts on Galaxy in order to play multiplayer at all. There's not even cross-play with Steam, which makes me wish I just bought it there.

Added to the mandatory Galaxy list:
THE KING OF FIGHTERS XIII GALAXY EDITION

But what about offline split-screen on this one?

Thanks for the heads up, added to the respective list as well.

Any info about No Man's Sky?

If you are talking about the multiplayer, see here: no_mans_sky_next_update_now_live
Looks like possibly no multiplayer for the GOG version.

Sorry for the necrobump but here are some updates to the list.

Games that need Galaxy for online multi-player and check for unique store accounts before allowing MP:
The King of Fighters '98 Ultimate Match Final Edition (unverified)

Games that do not need Galaxy for currently working online multi-player:
Diablo Classic (Battle.net)
WarCraft II: Battle.net Edition

Games with local multiplayer via LAN:
Diablo
Diablo Classic
Star Wars Episode 1: Racer
WarCraft II: Battle.net Edition
WarCraft II: Enhanced

Sources:
https://www.eurogamer.net/articles/2019-03-28-warcraft-1-and-2-are-on-gog-today
https://www.eurogamer.net/articles/2019-03-07-gog-and-blizzard-bring-diablo-1-back-from-the-dead

Thanks, I added those to the lists.

Blood: Fresh Supply can be added to the next categories:
Games that need Galaxy for online multi-player and check for unique store accounts before allowing MP.
Games that can be played in multi player mode on a single PC via hotseat, splitscreen etc.
More details can be found here,

Crap! There goes the chance of the Linux port being released on GOG. :(

Added to the lists.