The license for the game is associated with your gamertag. You can even recover your gamertag on a friends console, download the game and play it. When your gamertag leaves that console, it will revert to a trial game. That being said, the actual license
for the game stays on your console. Not your harddrive, so if you change consoles you must be online to play the game. You can redownload you licenses, but Microsoft limits the number of times you can do this to one time a year.