No, regular games just sit around and wait for the player to do something. Nothing ever happens without the player actively triggering it. This is quite different from a movie, which will play from start to finish without the viewer ever lifting a finger.

I don't think there is anything that matches what OP is looking for perfectly, but games like The Last Express, The Legend of Zelda: Majora's Mask or Invisible Hours get somewhat close. In those the story plays out in real time with all the NPCs playing their roles, the player can observe and interact, but he isn't the central trigger for everything, the story will reach the end even without the player doing anything. Fahrenheit and most of the other stuff Quantic Dream has done also go in that direction, in those games you often switch characters, so you are really playing "the story", not a specific person in that story, however they are much more linear than the other games mentioned and don't leave that much room for exploration.

Haha you gave such a big explanation and invented games again. Still my point stands, all you are asking for is an interactive game that may not need user action to complete. But movies still need a script, without an actor performing an action the movie just doesn't complete it doesn't make sense at all. What you are describing is an open world like GTA, where NPCs just go around, gangs fight, police run behind, etc etc. It's just a game, it already exists. OP started with the expectation of an interactive movie. It's called GAMES.