Three Options to open NAT-Firewall
1. Get rid of the Router.
2. The gaming computer can be put on the DMZ.
It means that the Router can put one of your network's computers in front of the Firewall.
The computer is chosen by its IP number. Consult your Router's manual to the specific settings and menu.
3. Port Opening.
You can open ports through the NAT-Firewall and info can come in through these ports regardless of the NAT.
A. All Routers let you define few individual ports
B. Port Range - Most Routers let you define a range of ports to be kept open (e.g. 5000-6000).
C. Port Triggering (available in some Routers) - Applications that connect to the Internet by using port X expecting an answer through port Y. Port Triggering makes sure that port Y is available to receive the answer.
The way to open a port depends on the Router. Each manufacture has his own "Shticks" to go about it. Each one has his way of organizing the Menus. You have to read the Manual in order to know how to do it. The term that it is referred to could be Port Mapping, Port Opening, etc. In a Virtual Server.
List of ports that are associated with various applications can be found here:
Link:
Special Applications - Port List.