Even at G speeds, your router probably runs at a higher bandwidth than your internet can provide.
The issue at hand is latency: how long it takes for data to travel from your son's computer to the FPS game server.
A stronger signal improves latency (makes it lower). A reasonable signal from any router (above 70%) should be fine for gaming. Most competitive FPS players I've known always try to play at less than 80 milliseconds of latency. A good internet connection should give you something like 30-50 milliseconds of latency, the router will add AT MAX something like 5-10 ms latency. So, even in the worst case, your router is adding an imperceptible amount of latency to the game. Of course, this is provided you have a strong signal between the computer and the router.
Ideally, a DIR-655 should help by boosting the signal to your son's PC and stopping the disconnects. In the past I'd recommend it without question, I'm not quite sure what your experience will be with the newest models and the newest firmware. While the 1.33NA firmware (the newest) has corrected most of the issues I used to have with the DIR-655, I can't guarantee this will be your experience.