That's a good example to raise. Let's apply two different descriptions of what these kids are doing.
A) The kids are a story. Or perhaps their play is a story.
B) The kids are telling a story. Or their play fabricates a story.
Does our description turn everything into tomatoes, or using it can we still tell tomatoes from potatoes? Is our description progressive i.e. can we use it to move forward our understanding? If we say the kids are a story, I feel like we're stuck there. I've no idea how children can be a story and I don't really know what is meant by story, seeing as it is also children. It has a certain whimsical charm, but for me lacks analytical power. Because of that, I can't use it to better understand kids or stories. The description really, when you get down to it, takes us is all sort of odd directions.
On the other hand, if I differentiate kids from playing from storytelling from stories, I have a lot to become interested in. Is play the same as storytelling? That's a very meaningful question. What constitutes good story telling and how might I recognise a good story. I don't know about you, but for me really useful questions roll right on out of the description.
So in a nutshell that's how I approach this. Story telling happens in D&D, no question, but D&D is not a story. That latter description is a dead end. Maybe when the OP asserts "D&D is also a story" that's just poorly chosen wording. If so, fine. I'll back right down and say - "Oh, you meant does D&D include story telling? Right then, that's a worthwhile description to look into."
Does that help clarify/make sense?