Hello there, actually when you install a game, sometimes
the installer asks you which users do you want the game to be available. if you're on the admin account, it'll say something like "install this game just for me (admin)" or "install this game for everyone using this computer", that option will make the game available for every single user on the PC.
If you installed the game within a Guests account and installed it "just for you" it won't be available for the Admin
Hopefully that won't confuse you even more hehe