There are some games with brilliant stories that are open to interpretation, and done in a way that allows the player to discover the meaning on their own... The one that comes to mind is Braid...
The problem then with games is that you cannot have 'just story'... that would just suck... Imagine playing 'An Inspector Calls' the game... [footnote]It's a play which takes place entirely in a living room, with dialogue... nothing else happens, its just talking, but it is still a brilliant story about how every member of this particular family is linked to the psychological well-being of a girl who had committed suicide... the inspector himself is open to interpretation, and can be taken in many ways. Some interpret him to be a figment of the viewers imagination, and is only there to instil the conversation and make the family members realise their errors, where as other people take him as literally just an inspector, but one who really knew the families doings inside out... very clever story.[/footnote] The game would suck... you would only just keep pressing A/X over and over until game over... great! Braid itself had very clever fragments of story woven into it, and much of the game was metaphorical to the plot... but the game play itself, although brilliant, was very much irrelevant from a story perspective... What you get with games are fragments of story, broken up with action sequences in between, but this is good, as when you are in control, you don't particularly want to try and focus on an unfolding story as well.
Take a game like Ace Combat, which often puts story in dialogue that play through the in game radios... you can hear TV reports, and ground forces, and even sometimes the enemy... it portrays characters feelings of events that you are watching from 10,000-30,000 feet, and would have therefore been to far from the action to care. The only problem with this is that myself, and I imagine a lot of other players miss lots of this dialogue when they play, because they are to busy being occupied by dogfighting, trying not to crash, and racking up points, to notice the news report of the president escaping in a helicopter...!
Other games which focus on game play and story like Stranglehold, Metal Gear Solid or The Getaway do it brilliantly, but when you look at it, the bits you play are essentially just transporting you to the next bit of story, and you playing has little to no effect on the story what so ever... You know Hammond in the Getaway will get to his son just in time, no matter how many times he stops to have shoot-outs with the police, causing mass genocide, or acting like a spastic and getting repeatedly run over, on the way.
I can see what Jaffe is implying, but I think he went about it in too much of a broad-brush sweeping way. I think what he was implying is that the types of heavy hitting stories, that you find in other types of media, are not suited to the gaming world, and that other developers should stop kidding themselves that they are actually creating something more than they are.
Personally I disagree with this. I think that we are just yet to see real stories told in games, where the players can discover it themselves, and where the pace is set just enough that the story is more involved with the game play itself... Until then I look forward to more simple, yet effective story telling through cinematic events, set pieces and cut scenes.
EDIT: On another note, does every game need a good story...? I see they try and inject stories in the strangest of places now... Like the new Tiger Woods where you start as a kid, and learn golf with the character as s/he grows up... Do you actually need that, or should games like that just stick to what they are good at...? The action?