Here is my situation:
I have a bro that also bought the game on GOG, and we would like to play Co-Op. Both of us are using WIn10 64 bit.
(we are both connected via LAN cables to our Router).
Unfortunately, some strange issues are happening with the multiplayer.
One of us connects to the host computer's IP address (Using the Default Connection Method), and attempts to connect.
Weirdly enough, the host's game only shows up on the browser for about 11-15 seconds before disappearing completely for anywhere between 20 and 60 seconds before the same thing happens all over again.
Once, my brother timed it right and got to wiggle around a little in game, but then he got dropped out moments later.

What can we do to actually get on LAN and play together?

Wondering the same. Assuming I might just have to use Tunngle or Hamachi anyway, even though we are on a LAN.

EDIT: I apparently answered my own question 4 years ago (which must've been the last time I tried to play this game) in this thread. My brother claims that thread was intended for a LAN party, which implies I was never able to get it to work locally, and I had to use Tunngle (i.e. a VPN).