The structure of Shrek the Third
is pretty typical of action/platformers. You run around fairly constrained 3D levels attacking various enemies, breaking boxes and other objects to collect fairies, coins and other pickups while trying to reach some boss. I referred to the levels as "constrained 3D" because while you can move all around, there is typically a very specific path that you need to move on in order to progress. While there is room to move toward or away from the camera, it stays locked in almost a side-scroller fashion and you are almost always moving from one side of the screen to the other. In the end, this leads to very linear levels that don't require all that much exploration, but are not really boring since there is a pretty good flow of obstacles and enemies to keep you occupied.
The story of Shrek the Third follows that of the movie, mostly anyway. Where the film has Shrek and his gang roaming the globe looking for the next king of Far, Far Away, Arthur Pendragon, the game pretty much jumps to the shipwreck that occurs on the groups' trek back to Fiona's homeland (a good third of the way into the film). Now Shrek, Donkey, Puss and others will have to take down major villains like Hook and Prince Charming in order to get back to the kingdom.
Shrek the Third also sports a multiplayer mode that lets you and your opponent attempt to knock down each other's castles by lobbing various objects at them via catapults. While mildly interesting, this game has a bit of a tacked-on feel and loses luster quickly.