Hmmm. I'm guessing that was a game mechanic decision...of course, they had kind of a free hand because, as some website said, "The third movie has a mutant war sooo big it almost involves some of the characters we saw in the other movies"
Just remembered: the so-called X-Men: The Game actually takes place in between the second and third movies, and explains why Nightcrawler is not in the third movie.