I think it's as Straykat says: they're hardcore, combat-focused games that people finish to get gamer points for having beaten it.
You might have something here: if the story only supports combat, like in Diablo, for example, and the main goal is to level up your character by fighting more and more difficult bosses with one final super-boss, AND (it's important!) developers did not overdone it, then chances are more people will finish the story.
It also explains why ME2 was completed more times then any other game in the series - you are truly building up your character and your team (and ship as well) for one mega-battle. Everything is counted, everything you worked for is used at the end and needed. You see the result of your work there and that final battle truly is the culmination of the game.
While in ME1 you are more wandering around, your team is there just to talk and comment, but you have the story . And in ME3 part of the frustration with the endings is coming from pointless journey and complete ignoring of all your work on the way (those points you accumulate is the only outcome).
I was raising it as a counter to your claim that if more people finish the game, that must mean the story is better.
You talk about movies and I see it more like books. In the movie theater it is unlikely you will leave or fall a sleep, but if the book is not interesting you might throw it away without regrets. Same with the game - again, STORY driven game - it you are not engaged with the story, you leave that story. And same with the book-writers it indicates the fail of the story.
There were games that I finished despite deeply hated combat system only in order to see the story. And there were games which I did not play through only because stories were too lousy to pick my interest.
Sure, some people are looking only for an interesting combat and do not care about the story, but I do think another type - the one seeking story first and everything else later does exist as well (I am one of them). Can not say if one group is bigger then another, but for "story-type" gamers completion does equal success.