On the same router, you should be able to use LAN without VPN software.
Have either of you tried playing with anyone else?
If you can not join other people, either, try starting the game, switch to windowed mode and lower the game resolution (and maybe check the option to mute the sound volume when the game doesn't have focus), start a multiplayer game, hit Esc, open the Connectivity Menu, optionally disable online multiplayer (if it is enabled) and make sure LAN Connections is enabled (or that can be done in the options before starting a new game).
Next, start the game again from the 'EoCApp.exe' program file (doesn't matter if the first instance is started through Steam/Galaxy or the executable), select Join Online Game in the Campaign section, switch to the LAN tab, rather than Online, and try joining.
