"We need to deliver our story in a way that is uniquely video game,"
This is the key to what he's saying; not that there should be no story, he just doesn't think filling in the story as a wall of text (or lengthy speech) is the way to do it.
The problem with implementing this into an MMO (most current ones anyway) is that the designers are limited in how they can tell the story through subtler, more interactive ways. the requirement that all the thousands of players on the server must be able to have the same experience means you can only do so much to directly involve a player in the story. from what i've heard (i haven't played WotLK) blizzard made some steps forward in this in the latest expansion, using instancing to create more immersive interaction with quests.
imo, the only real way to do this right is to have procedurally generated, unique quests and decent AI. when a player does one of these quests, it stays done and the effects persist in the world (the village you saved recognises you as a hero, the burnt out goblin camp you destroyed remains). i think this is the ideal of what Kaplan is talking about: you don't need the quest givers to say anything other than 'omg, goblins ate my baby!', you go searching for their camp, pick up their trail (chewed baby parts?), maybe bump into and join forces with some other players, get ambushed on the outskirts of their camp, fight your way into it, maybe find a note on the cheiftans body which spawns another dynamically generated quest, return to the village a hero. thats how you involve characters in story in a game.
this may sound like a standard WoW quest but imo the experience instantly loses any sense of 'story' when i see the whole goblin camp respawn behind me as i'm striding away, or get back to the village, get congratulated for my victory and then see the quest giver wailing about her poor baby to some other schmuck. when i come back through the village in 6 months time and the village hails me (only me!) as their hero and offers me their daughters, and i'm like 'oh yeah, i remember this place', THAT is story.
i recognise the technical challenges of this but i think the tech is feasible for the next generation of MMOs.