If the the rest of your electronics in the house are using wifi just move the modem to his room so he can hard wire into it and if you need to upgrade your wifi to reach the other devices then that is better than some of the alternatives. Otherwise if it is possible move the modem somewhere in the house where it is feasible to run some cable into his room somehow. I'm not a gamer myself but anyone who is serious about gaming will notice a difference playing over WiFi vs hard wired into their internet connection.
That's one thing if I were to ever build a new house (which I hope I never have to do) I would wire Ethernet ports to any place in the house that may have a device that will connect to the internet so basically every bedroom, living room where your entertainment devices will be at, basement, etc. Wire it all into a multimedia closet in your basement and enjoy stable connectivity. Have friends that did that and are glad they did