Lots of games tell stories these days. There's no fundamental reason those stories couldn't be adopted to the silver screen. Of course many of these stories aren't really very good, but the same can also be said of any medium. There are elements that might not translate, but that's true of any adaptation. For instance Bioshock's infamous "Would you kindly" plot point won't come though the same way in a movie.
A movie needs a couple hours of focused plot, and a limited number of in-depth characters whose motivations can reasonably be covered in this short time. A blockbuster game generally involves a much larger cast of characters, and a much, much longer/wider plot story to cover the hours.
If you leave the story as-is and just cut the "sidequests", then the movie will be full of characters who are barely introduced and whose motivations make no sense to those who haven't played the game and don't know the backstory; and if you cut the story to be "movie-sized", then it will have little resemblance to the original, as key points will need to be drastically altered.
FFVII: Advent Children is a great example of this. Half the characters from the original game just come stumbling into the plot with no introduction or explanation.
And books often are even harder to translate the story aspects for because they usually take place over much longer time spans than movies or video games. Many movies made from books seem to have character relationships that seem like they should have taken much longer to develop because of it.