aborsodi: I have experienced the same troubles as you. Initially I thought the problem was my perimeter firewall. To test this I used the VPN client that comes with my Norton 360 AV. I live in Norway so I set the VPN region to Norway and launched GOG Galaxy. The result was the same, but I decided to test another region and changed to Sweden. Now everything works. To test some more I changed again to the UK and it works. Changing back to Norway or disabling the VPN reproduce the problem.
I have also:
1) Changed DNS to the Google DNS’ and others.
2) Disabled the IPv6 with the GUI.
3) Set IPv4 to be preferred over IPv6.
4) Disabled the IPv6 stack and all its functionality.
None of it works, except for the VPN.
I do not think this is a GOG problem, to me it feels more like a routing problem.
I was also thinking about a routing issue. Tried your recipie, using NordVPN connected to Poland. Clicked installed and right away it startet downloading and installing. Installed two games when connected to Poland by VPN. Disconnect = server error message right away. I too live in Norway,