Movies afraid to deviate away from source material I don't think applies to the problem. I've probably seen most video game movies (even the cringe-worthy Uwe Boll ones) and I'd say the overwhelming problem is no one on set even bothering to look at the source material, or understanding what they're trying to do.
Someone mentioned Edge of Tomorrow, which never was a game. It was based on a very light-sci-fi japanese novel, in turn inspired by a player's forum account of restarting a game over and over in order to incrementally learn enough to finish it.
But it doesn't really matter whether Edge of Tomorrow was or was not based on a video game. The fact that it works as a movie and you can think about it in terms of a video game proves that there's no issue with making a video game movie.
The problem with Hollywood sometimes or often putting out crap is a Hollywood problem, not a medium or genre problem.
Think of a movie you thought had all potential to be good, but turned out bad, and then google the backstory on its production. I'll put $10 on saying that it most likely suffered from "too many chefs"/creation by committee, and focus-grouping it to death, instead of trusting the vision of the creator(s), whether that be screenwriter, director or other.
This is obviously subjective, but why is the best Marvel movies Guardians of the Galaxy, Ant-Man, Deadpool and Logan?
For example, James Mangold did both The Wolverine and Logan, what changed between them?
Some games can even continue story telling for hundreds of hours, meandering through dozens of different storylines, arcs, characters, minute details, (Skyrim, Fallout,..). Some games even have their own books inside the games that the character player can read!
The medium really is quite a bit more flexible than a movie. Where I think some comments are suggesting that games are not story rich enough to translate into movies and that's certainly true in some cases, I would argue that the types of story telling are simply not always directly compatible with a linear movie story line.
In a video game situation most of these people need to look at the game and build a world that looks like it’s ripped from the game, or the fans get cranky. But once the director does this, isn’t he/she tainted by the source material?
Books like Eric Nylund's Halo: The Fall of Reach, Greg Bear's Forerunner Saga (Halo again), or Brandon Sanderson's Infinity Blade: Awakening are all pretty well-respected and did well in terms of sales. Probably because they manage to avoid falling into the temptation to simply recreate the game experience as a book. They use the game's plot as a starting point to influence the story without dictating it.
Of course, by deviating away from "the game" as fans experienced it, you risk alienating them because the final product doesn't match up with what they expect. And because the same fans are probably the reason why the studio is willing to finance the movie in the first place, I can sort of understand why Hollywood repeatedly tries to hew closely to the source game even though that approach has repeatedly screwed them.
The peculiar thing is that they face a somewhat similar situation when they turn a book into a movie. And yet, Hollywood is more than willing to take risks and deviate away from the source material when necessary. So what about video games in particular scares the studios away from doing the same?