That is a misleading message from the online game browser. There are no dedicated servers for the game and it does not show games in progress, only lobbies. So you have to either get really lucky and search the right playlist while someone has a lobby waiting to start, or you have to fill up your friend's list with "Bird People" and join their games.
We recommend option #2. Check out this thread:
http://forum.1cpublishing.eu/showthread.php?t=15379
Post your gamertag or PSN... thingy... and send FR's to others listed. You will almost always find folks online to play with using this method.