Shadow of the Colossus also won the best action and adventure Bafta.
The event was hosted by TV and radio presenter Vernon Kay and the ceremony is to be screened on E4 and Channel 4 at a later date.
The sports award went to Fight Night Round 3 while the simulation prize went to The Movies.
Other winners included Electroplankton for best audio, Tomb Raider: Legend for best original score, Guitar Hero for soundtrack and Dungeons and Dragons Online: Stormreach for multiplayer.
The innovation prize went to Nintendo DS title Dr Kawashima's Brain Training: How Old is Your Brain?.
