App Store saids the App is installed but isn't?

Dear Apple Support Community,

Recently my brother has recieved a game as a 'early' Christmas present from his best friend. Now that he has recieved the game, he had the urge to clean out his MacBook Air memory to install the game with spare space left. Since my brother had been using the app store with my account, he asked me to log in and check the apps he had downloaded and to see whether he need them or not. When we went through all the games, he realized one of the games he installed wasn't on the purchased list. Since our parents put on parental controls on his computer, we thought maybe that was the problem and tried to turn off parental controls on his account. But it still had the same problem.

Then we went on and did some research on the internet, and we tried the following:

-Deleting the .plist from the preferences

-Deleting the application support app file

-Option+Clicking the installed button

Please help me figure out a way to remove this app from his computer and open up some space please!