Then the user account will have some kind of restrictions in place so the children don't play to much. I don't know if Windows has some kind of parental control instruments on board that might limit the use of specified software to specified uses per day, but maybe have a look for some restriction software installed on that computer.
You could also ask the school if they implemented such restrictions, because I can't think of anything else, as Hearts and Free Cell are games included with Windows and not Demos.
Is there some kind of message that pops up when you cousin wants to open a game for the fourth time?