Since it's going to be completely linked to the movie and like a part of it altogether, i expect it to cover up certain details that are only mentioned or left vaguely explained in the movie. For example, let's say they talk about in the movie about certain characters going through an event inside The World while the main characters were just somewhere else...you only get to hear that little talk in the movie, but in the game you'll be able to play as those characters and explore such events directly, learning more about them and clearing up some others details as well, and enjoying them through gameplay instead of just watching them like some bonus clips. That, or maybe certain events in the movie will become playable; a battle against some boss-thingy, for example, which you get to see in the movie as the characters attacking with random stuff and then finishing with epic stuff, will become fully playable and it'll be all up to you to decide how to face the boss and what you'll use against it.
For the latter, however, i would expect the PS3/Blu-Ray version to be very different to the theatrical release, as it'll replace some scenes with the gameplay and add/remove several stuff to make it fit well. That might be too much to ask though, even more if it's truly like my current idea, which involves some switching between movie and gameplay almost completely unnoticeable. As opposite to almost all games which are lots of gameplay with certain movie-like stuff, i think of it as an entire movie with some of gameplay added to it, not alot of it to fully involve a level-up system or complex equipment, but just enough to be able to enjoy the battles and whatever else you do, and enjoying the movie in a different way through it, as you get to play an active part on the events rather than just watch them happen. But again, this could just be a crazy idea of mine, and even more unlikely than asking for a Hard version of G.U. with complex and strategical enemy AIs D: lol
Tolby's idea of having the game serve as the "final" part of the movie sounds quite cool, however, i expect the movie to be able to answer most questions and have a proper ending on its own, rather than keep a cliffhanger that would "force" the interested people to get the game or see stuff about it just to know how it ends. I don't have anything against the game leading to a final epilogue of the movie (and maybe the entire .Hack series overall) and clear up every detail that had been left vague until then, but only if the movie is given a fitting ending for itself.