Yes, different stories have different appeals. Mad Max Fury Road does not have the same appeal as Dilbert which does not have the same appeal as The Hobbit which does not have the same appeal as Romeo and Juliet which does not have the same appeal as a Sherlock Holmes collection. I literally do not understand what point you are trying to make.
What kind of gaming are you trying to describe? What are you talking about when you say that something "isn't a story"? Do you mean a hack-and-slash dungeon crawl? Because I think that things like John Wick would indicate that "a bunch of fight scenes with the exact minimum amount of plot necessary to understand those fight scenes" totally qualifies as a story.
I think the problem you have is that you are misunderstanding what people mean when they describe RPGs as "collaborative storytelling". The point is to provide a term for the action of playing a RPG, so that we can better understand how to make RPGs good and enjoyable. For example, the collaborative storytelling perspective would suggest that part of making an effective RPG is providing a mechanism for synchronizing players' expectations about creatures and objects in the world so different people can make action declarations to interact with the same things in a coherent way.