What "story" means for a player: "I don't want to feel like I'm just pushing buttons. I want to be immersed in the illusion of really doing something".
What "story" means for game developers: "Do not let the player do anything. Force him to watch a lame movie instead of playing a game. Make lame unskippable cutsenes, then fill it with Quick Time Events. Make a close corridor so the gamer can't do anyting but exactly following our lame script. Don't let the player actually using the cool toys, just show them to him".
What the game experience ends being: "I'm just pressing a button for the [strike]game[/strike] script not pausing".