I would say that some of the hardest parts of achieving this in an RPG is that the players have to be skillful as well. They are responsible for so much of that stuff, and if their input is missing or inept or unworthy, it doesn't matter what you do with the villains, setting, and chorus of the story. In fact, the meta-story of the RPG, whether we are talking about Knights of the Dinner Table, or The Gamers 2: Dorkness Rising, it's this conflict between the DM's desire to tell a great literary story and the player's ineptness or lack of interest in that as a goal or even perception that the DM's goal is orthogonal to their own is often the driver of conflict in the story.
I agree on the weight of a/the player's impact. I won't necessarily consider "skillful" to be a nessecity, but I know what you mean. Being a good enough roleplayer to be able to invest (maybe even emotionally) in your character and his/her environment and fellow PCs. It usually suffices to have that "latent talent" hidden within a player if he/she somehow ends up in a story he/she particularly likes.
For an example, I've had that one player some years ago who was utterly prone to doing seemingly nonsensical actions, changed characters like clothes and didn't seem to really care about his surroundings (PCs were okay, but he was reeeeally testing his limits when it came to his DM-PC interaction). Then one day I tried DMing for the first time and said player was suddenly playing one of the deepest and most thought-out PCs who even fell in love with an NPC (who turned out to be a goddess without powers who was suffering from amnesia) and went to the end of the world to help her. I was more than pleasatly ssurprised to see our previous chaos-monger so utterly focused and invested in the campaign.