how we are actually supposed to write a story that can be turned into an actual game.
You can turn any story into a video game, the issue you'd need to deal with is how the gameplay would be. There are many answers to that. My suggestion is to play or at least watch story heavy video games and see how their story is delivered.
At least in terms of the style that takes 2-d art and the story combined with minigames.
I haven't tried nor seen Bunny Graveyard yet but I suggest that you not to stick with minigames.