Touwa: "NOTE: The game does not currently support multiplayer but we are working on resolving the issue."
Also you can check in the games gamecard
https://www.gog.com/game/empires_dawn_of_the_modern_world If there is no "multiplayer" listed in the Features tab to the right there is no reason to expect it will work in game.
GeneralSturnn: Some games(like Call to Power II) Say the same thing, but with various tests I have made(with my own computer here, a Windows Vista in the living room and Windows Vista Laptop) Multiplayer worked just fine.
As long as LAN and/or DIrect Connect options were not removed when GOG was able to sell it, then multiplayer should work with little to no problems, but, computers being computers will sometimes not register.
Edit: I did check it before I asked this question, but my past experiences is what had me ask if LAN/Direct Connect were removed or not.