Looking at how popular some games are nowadays they are popular because of the great storyline, characters and amount of interaction within the game. I found that through the games i've played the storyline is most important because thats what draws a person into playing. If theres no great storyline then theres no great depth of interaction during game play.
The final fantasy games is one example. And one of the most popular final fantasy games is Final fantasy 7. Everywhere i look theres fanart, cosplays and people talking about Final fantasy 7. A couple of days ago i watched Final fantasy 7: Advent children and i can see why the movie alone was good. But the game itself is better because of the storyline as well as the game play that keeps us hooked til the very end. And because of the success with Final fantasy 7, theres a prequel called 'Final fantasy 7: Crisis core'. Although i havent played it, it is still as popular as the original.
As a player i would like to make the story happen rather than let it happen to me. If you can do that then the game will be more interesting because you dont know who its going to affect the end of the game. Like on Disgaea: hour of darkness, depending on what you do during gameplay will determain how the game will end. MMORPGs like World of warcraft are different, because there is no storyline, you just play how you want to although your doing quests and fighting monsters. My answer for the last question: "Is call of duty a war story?" is: I have no idea. I don't like games like that. So i am going to take a random guess and say that it is because of the title.