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Added to LAN:
Dying Light

Added to Galaxy only:
Homeworld® Remastered Collection
Homeworld: Deserts of Kharak
Serious Sam's Bogus Detour
Post edited June 23, 2017 by Klumpen0815
Starbound has a separate server hosting software.
Shadow Warrior 2's multiplayer needs Galaxy but can be payed offline without it.
Incredible Adventures of Van Helsing 1 has online multiplayer not bound to Galaxy and also working LAN. At least it had, when I was playing it about year ago.

Not tested the later Van Helsing Titles yet.
Added:
https://www.gog.com/game/gauntlet_slayer_edition
Post edited September 11, 2017 by Klumpen0815
Since all Discord servers including the GOG related ones are mostly used for Steam and talking about Steam, I made this one, maybe we could even set up a few games of Screencheat, Invisigun, Mega Man 8 Bit Deathmatch, Scorched 3D, etc... there:
https://discord.gg/fs2vyaq
Post edited September 26, 2017 by Klumpen0815
Added Tooth and Tail to the "Galaxy dependent" list.
Any more to add?
Added Aragami to the list of shame.
Star Wars: Battlefront II
GOG provides two kinds of installers for this game.
One use Galaxy to support crossplay,
another is XP and Vista compatible, no Galaxy-based multiplayer mode.
For all the games listed in this post, direct play over the Internet requires the players to determine the host IP address through external means (IM, Discord, Mumble, etc.). While less convenient than an in-game matchmaking service, this is excellent future proofing, since it does not require a matchmaking service to continue running year after year.

AI War: Fleet Command has direct-connect multiplayer without GOG Galaxy. Guests enter the IP address of the host, then communicate via UDP on a player-chosen port (with a default provided by the developers, but configurable if players so choose). No dedicated matchmaker is provided by the developers.

Baldur's Gate / Icewind Dale are listed as local multiplayer via LAN. This is not wrong, but is incomplete. Some LAN play games insist on discovering the host via broadcast. These games allow the player to enter any reachable IP address, so they can be played over the Internet without Galaxy.

Descent+Descent 2 (no longer available for sale, but still available to customers who purchased before removal) predate Internet multiplayer as we think of it today, but their assets can be used for the source code ports Descent-XL and Descent: Rebirth, both of which support UDP play over the Internet. The source ports each include their own matchmaking tracker. The source ports cannot cross-play: all users in a game must be on the same source port.

Sins of a Solar Empire: Rebellion has direct-connect multiplayer without GOG Galaxy. Guests enter the IP address of the host, then communicate over TCP. Guests can configure the join port, but I don't see an obvious way for the host to configure the listening port. The publisher provides a matchmaking service.
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advowson: snip
Thanks for helping out.

Added to following lists:

non-Galaxy online multi-player:
AI War: Fleet Command
Baldur's Gate
Descent
Descent 2
Icewind Dale
Jazz Jackrabbit 2
Sins of a Solar Empire: Rebellion

Single PC:
Jazz Jackrabbit 2
Vikings-Wolves of Midgard requires Galaxy for online play.

However it also supports LAN play and Couch Coop with or without Galaxy.
Post edited December 03, 2017 by Hikage1983
GOG updated Battlefront 2 to use Galaxy for online backbone.
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Hikage1983: Vikings-Wolves of Midgard requires Galaxy for online play.

However it also supports LAN play and Couch Coop with or without Galaxy.
Added, thanks.
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DreamedArtist: GOG updated Battlefront 2 to use Galaxy for online backbone.
Also added.
Dafuq, when did this happen?
I probably don't have the old files anymore.
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Hikage1983: Vikings-Wolves of Midgard requires Galaxy for online play.

However it also supports LAN play and Couch Coop with or without Galaxy.
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Klumpen0815: Added, thanks.
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DreamedArtist: GOG updated Battlefront 2 to use Galaxy for online backbone.
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Klumpen0815: Also added.
Dafuq, when did this happen?
I probably don't have the old files anymore.
Found it here look at this, https://www.gog.com/news/star_wars_battlefront_ii_now_supports_crossplay
Post edited December 03, 2017 by DreamedArtist