Except the narrative isn't shaped by whatever the player does in any game where the player has freedom to do anything other than advance the story. Does killing random pedestrian #1 have an effect on story in certain games that allow it? Sure, it could. Does killing random pedestrian #5407 have an effect on story in those same games? No, it doesn't. Similarly in HL2 (I would assume, I've never played the game (I get horrible nauseous in FPSes)), you undoubtedly have the ability to do thing within the gameplay that ultimately have no effect on the story as it's told. If the player does nothing but goes on a rampage for an hour or trod back and forth looking for a given easter egg or hidden weapon or, hell, just admiring the scenery, it doesn't affect the story, only how it's told. Similarly, getting the player to fulfill the role of killing enemies doesn't improve the storytelling, even if killing enemies is part of the story; especially if the point of getting the player to do that is so the player can have fun, which is the point in almost every video game in which killing things is an included mechanic. They are _games_, after all. I'd like you to step back for a moment and ask yourself whether the openness in GTA or the sheer number of enemies you can slaughter in HL2 really makes sense within the worlds those games try to present, and whether distracting yourself with sundry pursuits really enhances how the story is presented.
Your absolutely right when you say that storytelling can be interactive, but the problem is you're applying the idea to the wrong medium. You see, video games, as they exist today, are an inherently "dead" medium. They're finished products which are delivered to the consumer as is. Technically there is some life in modern games--updates and multiplayer interactivity ensure that things can change; but where the story is concerned, once the game is on shelves, it's really no longer changing, at least not in terms of its interaction with its audience. Any reaction the game makes to the player has to be predicted by the developer and implemented during development; and with current limitations of technology, budget, and time, there simply is no way to make a game (or a game's story) that can react to anything the player could do. "Living" media, like plays, a storyteller, or a DM, have the capability of changing to accommodate the audience, making the story a more fluid thing. In games, however, even ones as open as Skyrim or GTA, THE STORY is something set in stone, no matter how many possible outcomes are recorded there. Every story-relevant choice you make leads to a set outcome; and in addition, the more variables you include to allow player interaction, the less control the developer has of making sure the player's interaction has anything to do with that set STORY.
Now the player can choose to interact with the game in a manner that he feels interacts well with the story, even if there isn't necessarily any indication or reaction from the game to enforce the idea; that is to say, he can roleplay and use his roleplay to enhance how the story relays itself to him. The problem with this idea is that it's on an individual basis, and most players refuse to sacrifice very much in the way of "fun" in the name of "story"; in addition, there are only so many roles the player can fill in any given game: Dragon Age, for example, even though it tries its hardest to encourage a wide variety of roleplaying, doesn't really allow you to play a character that conforms to the Chaotic Neutral archetype in a way where the world (or even your companions) recognizes it at all.
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