This is shaping up to be a typical Narrative rpg thread. There isn't a consistent definition of what a narrative rpg even is. We go back to Ron Edwards' exercise in academic discussion and find that games calling themselves Narrative rpgs don't fit that definition. Somehow, even decades later, we treat what Ron did as being objectively true. It's just a theory, and one I disagree with. D&D's playstyle is something he called out, for instance as being actively bad.
There are a ton of popular rpgs that talk about being Narrative games let's let them have that definition. Fate, PbtA, Forged in the Dark all have that as a design goal and they are casting a long shadow on other games design. The more recent Fabula Ultima is influenced by a lot of those games. And Daggerheart is as well.
You can play just about any rpg as a Narrative game. You certainly can play D&D that way. Some games just have more built-in tools to bring it to the front of the house. If you remember the 100+ page discussion on Backgrounds in D&D, a lot of the posters were saying certain Backgrounds had Narrative effect. And there was a pretty sizable backlash against that.
With the 1.3 Daggerheart playtest, you see a lot more discussion of this style of play. I expect we'll see more of this going forward to make it more of an explicit part of the game. What I'd really like to see is more of how the players can work to shape the Fiction with mechanics, for instance. There are very decent rules elements on how the GM and random rolls can do that already, and there's some of it in character abilities. Let's do more of that, please!