The PC version of Shrek 2 was quite different than the console version, with simplified gameplay so that it would be more accessible to a younger audience. However, Activision decided that it should probably port the actual console version to PCs, since the tremendous commercial success of the movie might actually lure gamers to buy a second Shrek game. And so we have Shrek 2 Team Action.
As the game implies, the player has several of the film's main characters at his disposal and can often switch between them, a la Sonic Heroes. Other than that, Shrek 2 TA plays more or less like most 3D platform games with several added twists: some elements of rhythm games and some searching around, for instance.
The game follows the plot of the movie: Shrek and Fiona travel to Fionas' homeland of Far, Far Away Land to visit the parents. Shrek's in-laws, particularly her father, aren't too happy with their daughter's choice -- so the poor ogre has to fight his way to gain their approval.