I see the other game available on the LAN, and it tries to connect, but then it simply doesn't connect. It does NOT give any errors. It just says that I'm playing alone, that I'm not connected to GOG Galaxy, and that it's going to reload my character's game so I can continue playing. So, do I have to have GOG Galaxy installed and running just to connect via LAN?

My reason:
So, the developers of this rather decent game clearly modeled after the Far Cry series apparently made a silly design choice in my opinion. If you develop your power rank, the damage of firearms stays really low, like barely starting a game low. My problem is I have to do a difficult quest now fighting the armed guys who are normal humans, but all the rifles are at begining game damages, which means it takes me my entire supply of ammunition to kill a single enemy, if I can even manage to kill the enemy at all.

So, in short, I made another character, raised his survival rank, and kept his power rank low. Now, I need to use him to buy decent damage firearms to give to my main character so I can do this quest without having my butt handed to me constantly.