What version and desktop environment you're running?
Mint has three versions 13 Maya, Nadia 14 and Debian and five different Desktop Environment editions;MATE,Cinnamon,XFCE,KDE. Editing the menu is not the same on every DE. Without knowing which version and DE you're running we can't help you.
If, by chance, you're using the MintMenu you can right click on the menu button,navigate to games and use the new item button to add the game to menu.