I can think of 2 native solutions here.
Task scheduler will do what you want but I feel this is going to be very limited (although it may suffice).
Create a new task and in the New Trigger options choose
Begin the task : At log in
Then
Delay the task for N minutes
The action is to restart! There are 2 ways to do this...
Open notepad, and type in shutdown -s -t 60
. Save this is as restart.bat (note, it's .bat, not .txt). Then when you set the action in task scheduler, choose this file. This should also give your son a message that the computer is going to close in 60 seconds (change this value to give more or less time)
You can choose one of the actions to run shutdown.exe and provide the parameters
This of course isn't really a perfect solution, as you're not considering what happens if your son pauses the game to do extra house work like washing the dishes as it will still be within this alloted time. It also doesn't consider that your son could cancel the shutdown command, or can just re-log on, but I get the impression this isn't a parenting issue, more of a "reminder" to help him!
You may also need to consider state - although he has a reminder that it will shut in 60 seconds, it may not be enough if he is part way through a game and has to reach a saving point, or there are multiple applications open where each needs to be saved etc
I think those using Windows 10 can use use parent controls for what you describe as it will provide ways to limit the amnount of time by application. It may also provide enough of a hint to see if 3rd party solutions exist for Windows 10
https://www.howtogeek.com/225323/how-to-add-and-monitor-a-childs-account-in-windows-10/
Those on Windows 7 have some control http://www.dummies.com/computers/operating-systems/windows-7/how-to-activate-parental-controls-in-windows-7/ although this seems limited
There are software tools for this type of thing as well but I'd suggest you ask at https://softwarerecs.stackexchange.com (just don't cross post).