From Wikipedia
Shrek is a video game based on the first installment in the popular movie series. It was released exclusively as an Xbox launch title on Wednesday, November 14, 2001.
This is the first Shrek video game to be rated T for Teen by the ESRB.
Story
Shrek takes place after the movie. Shrek and Fiona are married and living happily until Fiona is captured by an evil wizard, Merlin, who has placed a seemingly impassable fog to guard his fortress. The fog can be breached by completed good deeds. The Magic mirror gives Shrek a mission book which guides him through the lands.
Gameplay
The player completes objectives ("Good Deeds"). In most objectives, the player hunts for an object and completes an action. Not many objectives vary from this, though a few will occasionally vary. Notably, Shrek's ally and best friend, Donkey, does not appear in the game, neither is he mentioned.