user accounts/system settings and you can create different accounts in Ubuntu. You did not specify what game though. 3 gigs of ram, I assume it's a simple type learning game for kids.
Being a big gamer even today, a few years back games would ask if you wanted to install for All users, or just Admin for windows. Now, modern games just install as having access to a game is not considered a security threat, so all accounts have access to it.
For admin only the shortcut is places in the Start Menu, for all uses it's placed in Start/all users in windows you can just move the shortcut.
Whatever the case, the game needs to have it programmed in the install to select different accounts to write the registry keys.
If you have several accounts on windows for example, you can right click on the .exe and then the security tab then flag permissions for each account as an Admin. This will allow only certain accounts access to the program.
Ubuntu:
Where the game folder is, there should be some right click option, then an option to share contents in that folder with other accounts. These are for programs that install without root in Ubuntu. If the game installs without root, it's only available under the account in which it was installed. Games installed from the Software center should be available for all users.
https://apps.ubuntu.com/cat/applications/precise/software-center/
Right clicking on the folder the game was installed/ properties should give you options to share the contents with other groups.
Why not just windows?
Blessings.
