Parental controls not showing certain applications

Most likely the game is installed by drag and drop. Therefore, it is owned by you rather than by the system. If no one but your son uses the game then in the Home folder of his account create a new folder and name it Applications. Put the game into that folder. See if that fixes things for you.

If you wish to leave the game in the system's Applications folder then the solution is a little more difficult. You need to change the permissions of the application to match the permissions it would have if the game had been installed by an installer rather than by drag and drop. To change the permissions you must first select the game's icon. Press Command-I to open the Get Info window. At the bottom of that window, you will see the Sharing & Permissions panel. If the panel is not descended then click on the little arrow icon beside the name. You need to first click on the lock icon on the bottom right. Enter your Admin password when requested. You need to change the game's permissions. Open the Terminal in the Utilities' folder. At the prompt paste the following:

sudo chown root:admin /Applications

sudo chmod 0775 /Applications

Press Return after each line. You may be asked to enter your Admin password. Enter it at the prompt. It will not be echoed back to the window so type it carefully. Press Return again. See if this fixes the problem.