OK, I'm confused now. I thought that there was a thread earlier with a person who was saying they could only play the Demo version offline and the reason you gave was that they were playing on an Xbox that the game had not been purchased on (XBLA, not disc), so it had to be able to check first online to verify that the profile was the one that had purchased the game before it would allow the full version to launch on that particular console.
Did I misunderstand your other post? I thought you were asking whether you needed to go online to play the downloadable game. The answer depends on which console you're using. The console used to purchase the game gets "locked in" via its unique console ID. This one never needs to go online for you (or anyone) to play your game. Any other Xbox needs to be logged into Live with the profile used to buy the game, in order to play your game.
It's all a lot different from when I first started playing video games, that's for sure! Whack the game in, start it up, play. Now it's whack the game in, sign in, change the rechargeable batteries on the controller, start up chat, screw around with your router settings until chat works, download your save file, start the game up and play! (Did I miss something :P)
Did I misunderstand your other post? I thought you were asking whether you needed to go online to play the downloadable game. The answer depends on which console you're using. The console used to purchase the game gets "locked in" via its unique console ID. This one never needs to go online for you (or anyone) to play your game. Any other Xbox needs to be logged into Live with the profile used to buy the game, in order to play your game.