Can you connect your machine directly to your cable or dsl modem? That would tell you if your problem is caused by the router. I would also completely disable your iptables for the first run. If this fixes the problem then enable iptables while you are still directly connected to your broadband modem. That wil tell you if the problem is iptables.
You might also want to look into QoS packet prioritizing. I'm not familiar with it because I don't play network games any longer. (Getting old.) I've looked at the setup for QoS on home routers though. It looks like you can do a lot of traffic shaping, for good or for evil.
I've heard that the Linux version of the Linksys routers has very little RAM. Maybe the router just doesn't have the horsepower required by these games. Now I'm just guessing.
And yes, I believe that you chose the correct forum. Sounds like a network problem to me.