I imagine narrative design is akin to a screenwriter adapting a novel for film, but with the added responsibility of assisting with the direction of camera and acting, scene settings and special effects. Suggesting a subtle change of camera from a medium view to a close-up shot as to capture the actor's nuances. Or checking to ensure that the crystal vase with red and yellow tulips is precisely placed in every scene. In other words, I pay attention to the small details that matter.
Narrative Design is a hybrid role that coherently connects the dots between vision (the story) and medium (the platform). Its usefulness is not limited to games alone as it can transcend to other industries. One that, if given the opportunity, may overlap to filmmaking whenever possible.
At any rate, I also focus on telling the right story for the medium and in the right kind of way. Writing examples are below. I recommend checking out my most recent project, "Jen's Adventure".