Your computer's IP is an internal IP that only hosts in your network are able to see. Your router's IP is the IP the rest of the internet can see.
If it is your router causing the problem your game probably requires a certain port to recieve information. You need to find out what port that is then log into your router's configuration and forward it to your computer. See your manual on how to do... Usually you need to connect to your internal IP with a one instead of the final number. Example: 192.168.0.6 would be 192.168.0.1
Hope this helps
