The time spent on characters is why it'd arguably work better as a television series, I've seen people convincingly make the argument that ME2 in particular feels arced like a good season of television.
I must be a bit too old school, because I just can't see video games as a true story telling medium.
And yet you liked Mass Effect enough to want it get its own film adaptation, and called the story 'gripping.' However one feels about the gameplay of the series (which I found improved markedly with ME2 after some missed calls with ME1, while ME3's multiplayer was largely frustrating) that it places so much emphasis on player choices - right from your character's gender and appearance on to their history and etics - is a major part of that story's appeal, and in itself
is a good example of how 'gaming' can tell meaningful and interesting stories. (Telltale Games' surprisingly excellent Walking Dead adventure game is another example of same.)