http://www.grimdawn.com/forums/showpost.php?p=436134&postcount=19

Guildie is thinking of buying the game & we need to work it if we'll be able to play together, but I've read that it's not likely.
galaxy is not an option, so hoping Hamachi does work.
Rumour has it Hamachi also makes steam-gog cross play possible.

I was the one that reported successfully doing it;/ but it has been a very long while since i played the game and so in good conscience cannot say that it works any longer as i like to be able to refer at the moment i give it it's blessing to be currently in the process of working.

I will say this Hamachi is design to show group members as part of the same Local Area Network; as in it is not an internet based multiplayer at that time it is a LAN game.
If you can get a steam version and GOG version of the SAME version no. into a normal LAN at home then you should have no issue with having Hamachi enable the same functionality between two computers on a ahem *Wider 'Local Area Network'.

Historically I have had issues with primarily Steam and Non-Steam games being patched at different rates (version mismatched); allowing no direct IP connectivity via inputting the IP, or features being locked to one platform (Dungeon Defenders).

If you want to ensure they both work; then you both have the legal license to play the game just copy the game folder over after they back up their steam version; this being why you purchase DRM free instead of steam.
You know so 'you' have control of 'your' software.
Being the same product means there should be no issues.