First of all Donnie Darko- weirdest and most confusing film ever. Anything with time travel in it hurts my head.
And secondly I'm sorry about the Reading thing again because I still feel really stupid about not being able to read those incredibly boring and picture-less books.
Anyway I feel that the story in a game is almost as important as the story of a film, and it really annoys me when people just concentrate on the graphics quality. Most of the reviews I read mainly talk about "how good the graphics are" or bad depending. I'm sorry but, yeah quality of graphics is important, as is game play, but how long can you sit in front of a game and go "wow look at that rock texture". For me, personally if a game has no story, then it just doesn't interest me. Which is why I don't like the Sims (and because its extremely boring, who wants to watch a character clean the dishes?)
However I don't think that just a good storyline could support itself on its own, people have different interests. I mean this is just me, when i first started playing Lara Croft on the PS1 i couldn't remember the storyline at all and half way through I remember asking my sister what the point of the game actually was. Those games in my opinion are more game play based. Needless to say, the Lara croft games aren't one of my favourite.
There are other techniques used with storytelling to also engage the player:
Techniques to get a player to identify with the character he plays;
Techniques to get a player to bond with an NPC (a Non-Player Character)
Techniques to give an NPC a quality of emotional depth, even if the NPC speaks just one line of dialogue.
Techniques to take the player on an emotional journey
The storyline of a game can help or make the above points happen and without a proper storyline, the above cant happen properly or to its full extent, therefore making the player more distant to the character and less appreciative to the game as a whole.
So in all I personally believe that the story is by far one of the most, if not the most, important part of a game. Coming either ahead or tying with game play depending on the players preferences.