I think this is very system-dependent.My goal is always to make gameplay about the dynamic story rather than the rules. But I've found that beyond a few basics, most players don't need to fully digest the rules in order to participate in building a collaborative story. Particularly if the genre expectations are understood, then it's just a matter of imagining your character in the fictional circumstances and describing what you'd like them to do. As GM, I can respond rapidly and adjust their sense of the fiction as needed
Some systems wear their genre on their sleeves and deliver genre-consistent outcomes. Examples I can think of that I've GMed recently: Prince Valiant, Cthulhu Dark). And both respond on good GM fiction-oriented responses and mechanically are relatively light (especially the latter).
Some don't, though, and outcomes can depend on mechanical features that don't particularly track genre. I would put many versions of D&D in this category. Traveller also can sometimes be like this.