The definition of 'story' remains contentious. The problem is, there are so many contexts that the term can be applied in - most dictionaries list at least seven discrete cases. When a word has taken such a diverse role in language, it is no longer possible for us to pin it down to a specific meaning - we have to accept the diversity of its application.
In terms of formal discussions of writing and game writing, the best solution might be to accept 'story' as a semantic umbrella term (like 'religion' or 'food') and to avoid using it when talking about the specifics. It's capacity to be used in this way explains why different people report such different things when we ask them to relate their 'favourite stories' in a particular context, especially for games where the scope of 'story' is even wider than most dictionaries allow!
I think perhaps that there is a certain sense to which the term 'story' has a fractal quality... it has that fractal property of 'self-similarity' - it has the same nature at all scales, like a leaf or a coastline.
An anecdote, scene or brief narrative account all constitute a 'story' on a small scale; complete chapters, episodes or narrative segments constitute 'stories' on a larger scale (they contain several 'stories' in the previous sense - many scenes). Above these, we have framing narratives which are also 'stories' (stories which contain stories...), and above this we have abstract narrative patterns such as myths and legends which are also 'stories' (which contain many different 'stories' - there are many versions of the King Arthur legend contained in the 'story' of King Arthur). At all scales, the term 'story' still applies.
In this way, a large scale story is made of many smaller stories, which in turn are made of smaller stories, and so on down to the smallest element of story - which might perhaps be a single scene. The word 'story', therefore, describes any and all aspects of the story experience, we can choose to see it as a fractal noun, applicable at all scales with broad equivalency.
And if we choose to accept this approach, we acquire some freedom to define more precise terms to supplement 'narrative' and 'plot' such that our discussions of story can have clearer meaning.