As a video game you control it, you can explore the world, you can increase or decrease the pace, you can blow through for a surface level casual experience, or you could find collectibles or logs that may expand on world lore, the type of stuff that is either wholesale more thoroughly expected from a book, or cut from a movie for pacing, these things can now be in a player's control on a case by case and player by player basis.

Parts of a story can be affected by choice, even when heavily scripted. Spoilers for The Last of Us, but near the end Joel is required by by the story to get Ellie back from the Fireflies, and you can justify his motivations for what he has to do to yourself or not, but at the peak moment where he actually finds her, after killing endless soldiers that fired upon him, he encounters surgeons who were about to work on Ellie. The player can decide for themselves whether they kill the surgeons or let them live, and not in a dialogue option way, but just based on whether you actually shoot them or not, and that choice can say things about both the player or possibly the player's mental image of Joel.

That's a relatively small example, but only video games can provide these sorts of small divergences in experience affected by player choice, and of course that experience is altered in the tv show version of that game, because its not possible to deliver it in the same way.

You play games to experience a mechanical challenge or expression of your intent and skill, but that doesn't mean other people don't go to games to experience story, whether that's a mostly pre-written experience like The Last of Us, or a story told by the player's statiscal build and gameplay choices, like Mount & Blade.

Even something you'd expect to be heavily pre-written, like a visual novel, can break the normal flow of time and events to allow or even require you to revisit previous sections and allow new choices that change the path and ending of the game, like 999.

What you consider the ideal video game just isn't what everybody does, and that's awesome because video games are such a massive and malleable medium that they can accommodate for all of that. You can enjoy Doom and Super Meat Boy, and other people can enjoy Phoenix Wright and Dear Esther. There's no art police that said three types of mediums are enough or ideal to express everything, the market and humanity decide that, and we decided collectively that video games can do story in new and interesting ways, too.