When a computer reqeusts information it does not use a port. Ports are only needed when you are sending data to a computer that did not request it.
In older games like quake3 the server computer would send data to each computer about where everyone is on the map (just as an example). Nowadays your computer asks the server "where is everyone on the map?" and the server sends the data. This means an open port is not required because your computer has asked for the data.
Basically most newer games will not need open ports. I know dawn of war doesnt cause I own it.