The listing in GOG indicates that you need GOG Galaxy to play "Online Multiplayer".

This isn't super clear.. does it mean only match-ups require GOG's DRM, while you can still play LAN or direct-by-IP games with friends?

i.e. Does GOG always have to be between players, or can players play using only Streets of Rogue?

I can tell you that the Linux version works with couch coop (2 players, 2 controllers, 1 screen, 1 computer). I'm not aware of a LAN version.

EDIT: I looked on a Windows PC and the multiplayer seems to have LAN in the options, though I have no tested it yet.

I can update this to say, happily, that LAN is supported by the Linux client and works fine: tested with two machines and was able to play multiplayer no problem. I see no reason this wouldn't work outside a LAN using a forwarded port or VPN also, so the short version is "no need for GOG/DRM to play multiplayer streets of rogue".

Thanks for the answer Magnitus, for some reason I got no notification of it and only saw it now.