I thought the game supported cross-platform multiplayer, meaning a GOG and a Steam version would work together through direct IP as long as both share the same game version.

FYI, you asked earlier if you could play co-op on the same computer and I don't think that's possible because it doesn't say Local Co-Op at Steam and that's a game feature, not a client feature.

The nature of the game makes this difficult as well. You would need two screens (or a splitscreen, which sucks on small monitors) and two mice/mouses (how's the plural of the computer thing? same as the animal?) and keyboards, since both characters can go into different directions.

What you could do, is to set both characters to "No AI" (every character can make own decisions in dialogue) and play the game "hotseat style" during combat and dialogues. That's how we played "multiplayer" in singleplayer games, twenty years ago :P

It's meeses.

I was able to run co-op on LAN with a single key, but you could run into tech issues. It is DRM-free multiplayer, though.

You should (unless it was deliberately disabled for some reason) be able to play on a LAN or via direct IP connection with the GoG version. Galaxy isn't required to connect; it'll just act as a matchmaking/player-finding service when it comes out.