Steam invites aren't supported for the game, and the steam multiplayer services in general aren't used. What you need to do is start a game via the host new campaign button, give your friend your public ip (make sure you've forwarded your ports -- info on that in the stickies), and then your friend opens ai war, goes to the join multiplayer game button, clicks direct connect, and types in your ip. I believe there are instructions in the game manual and on the network tab of the settings window in game.
Hope that helps!
