Zencoder, and others are right.
Your cheap...oops....inexpensive home router does support the UDP protocol. But it doesn't support allowing you to specifically route ONLY UDP (and exclude TCP, ICMP, etc) to any port you wish, unless you have the firmware version that does so.

Without digging further into your gaming requirements, this router may not work if the game you play requires multiple UDP or TCP ports to be routed.

Solving this problem should be easy enough.
1) Simply go to the games website or help files to find which ports must be transferred. Enter that into the router (don't worry about the protocol, just route the port numbers.). Point the IP address to your machines address. (Hint: This may not work if you are using this router as a DHCP server and you are getting your computer addresses from it) (Instead I would set both the router and your computer to a static IP, like 192.168.1.1 (router), 192.168.1.2 (computer).
2) Ensure your computer firewall is turned off or allowing both UDP protocol and the desired port numbers through.
3)If the game is setup right, it should work. Although, there are games that require a subscription before it ever allows internet connectivity, say, Asheron's call requires some MSN or some other gaming account first before they let you use your program to play. (I forgot the exact details, it's been a few years.)

If you've done all this already, then just forget what I've told ya.