Not going to happen. If it's TCP/IP, it's just a generic packet. The port # is what is identifying it.
It's not just the port number. If it was as simple as moving the port, people would have done it. Besides, there are a limited number of ports available for incoming connections (1024 - 65535), so there is overlap between applications.
A lot of those QoS filters actually inspect the packets to see what the content is and use the payload to determine what the application is. Consequently, certain things get a lower priority than others.
The only way to get around the filtering is to modify the contents of the packet. Obviously, changing the packet contents would mess up the game, so the only way to do that is to run his packets through a VPN. Some games will balk at that, some may not. He needs the aid of an outside server on the internet somewhere, and the pings are just going to go up with the encrypt / send through VPN / decrypt / send to game server cycle.
In short, he's probably screwed

I know some people at schools like that have gotten their own cable modem installation in the dorm, and used that for internet access. That wouldn't have been an option in my school, but I know it is in some.