Hi Fr4nkTheT4nk.

GOG.com is D.R.M.-free, but in order to play multiplayer, you need to create a Paradox account (as ussnorway mentioned). The Paradox account does not relate to your GOG.com account or your copy of the game.
Its sole purpose is enabling you to use the Paradox servers and create your multiplayer name-tag/profile, while making the process of multiple I.P. addresses connecting in the same lobby conviniently simple. Unlike other games, Stellaris does not use the A.P.I. of the GOG Galaxy client as middleware (like Steam does for every single game, except for some rare exceptions), to gain access to the Paradox servers, so you can enjoy multiplayer without any form of D.R.M. or server communication middleware.
Asking this in the Paradox forum is not a particularly good idea, in my opinion. Just hand-out GOG's offline installers of Stellaris to your friends and ask them to create their own Paradox account, to unlock multiplayer functionality.

Cheers.