I don't know the game in question but if I was to make an initial guess (that could be wrong by all means!), what could be happening is the router or wireless card is buckling under too many concurrent sessions which some games can tend to do, bit like what occurs on bittorrent.
What I would do first of all is connect to your router with an ethernet cable, bypass the wireless, and see what happens then. If the issue goes away, you have narrowed it down to the wireless part of the router or your wireless card on the laptop - then I'd try temporarlily disabling wireless security and see if any change happens.
If the issue remains, first of all I'd see if you can disable anything on the router which might add to additional overload on it, SPI firewalls, firewall rules, QoS, etc...
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