Two questions:

Do you know if the gog version of D:OS works with with CoOp-Mode with the Steam version?
And if yes, is anyone interested in playing with me (as I have the Steam version)?

Co-op can work but requires everyone to run the same version. This can be an issue with Steam since it auto-updates by default and receives updates straight from the developers, while GOGlodytes have to wait for a patch installer to be prepared and released (though this has happened within a day or two so far with D:OS).

So if you want to co-op with GOG players, you'll need to disable auto-updates for D:OS to avoid having your game interrupted by the next patch. Can't help with co-op myself since I'm a zombie-apocalypse-ready gamer who uses an offline system powered by hamster wheels and rubber bands. :)

1.0.81, same as Steam. There is usually a stickied topic at the top of the forum for the latest patch.

Thank you Raze_Larian!
Forgot about that... :)
I normally look for the version number in my games account - in the download section.