First of all, this is already probably the greatest video game adaptation of all time.
So, some shower spoilers are gonna come after this.
I had this weird clash with my ex-girlfriend while we were playing the game.
She insisted that video games were going to be the next innovation in story-telling. I insisted that they weren't.
I still think that I was right.
Just take it from the beginning.
In the show, Joel's daughter dies similarly to the way that she dies in the game. In the show, you have no control over Joel's daughter dying for obvious reasons -- television is what Marshall McLuhan would refer to as a hot medium. We don't interact with it, we just experience it.
In regard to the video game, you do interact; but, the story-telling element still needs to be told to you. There's no way to play the game in a way that prevents Joel's daughter from dying. It's made that way because the rest of the game doesn't work unless she dies. The game, which is generally a cold medium, still needs to have the hot medium component in order for the story to exist.
Yes, at some point, we're going to have platforms, mediums, and games that let us play exactly how we want, make the decisions that we want, and the entire world will respond in accordance to our decisions; but, that's still not going to be story-telling. In fact, it'll be the opposite. If there's a story that emerges, it will be entirely by accident.
Participation isn't a part of telling a story. Once you're participating, you're not in the audience.