Update: The original report was misleading - Crysis from Xbox Live Games on Demand does not require an always-on internet connection to play.
The lock-out timer described below only appears when playing Crysis on a second Xbox 360 console - a different machine than the one it was originally downloaded to. If the connection to the Live account drops, you'll need to recover the Gamertag within 10 minutes to resume gameplay.
Original, erroneous, story: You cannot play Crysis, bought from Xbox Games on Demand, offline.
The moment your connection drops, a 10-minute timer appears. That's the window you have to reconnect. Fail to do so and you're dumped back to the dashboard, reported MS Xbox World.
Presumably a similar always-on internet requirement will be present in the PSN version of Crysis, available today.
Crysis costs 1600 Microsoft Points on Xbox Games on Demand or Ł15.99 on PS3.