When should "histoire" be interpreted as "history", and when "story"? Are the two meanings distinguishable grammatically?
Well here you have a hint : if it was about stories (like tales), you would have : "Il a beaucoup de livres d'histoires", with an "s" (plural form). Because it is singular, you can hint that it is about History (in a sense of what is past). I think that should be a pretty good indication of when to use each one.
If you need anything else...
I can't agree with your analysis. A story book can be a book with just one story, in which case it would be " un livre d'histoire" and several of them would surely be "des livres d'histoire"
"Un livre d'histoire" is a history book, nothing else.
"a story book" is either "un livre d'histoires" or (more commonly) "un livre de contes".
But if it's a listening exercise, how can you tell? Isn't the pronunciation the same?
Again, we would probably not use "un livre d'histoires" in plural if it were a book with several stories in it. It would be "un livre de contes" (storybook) or "un livre de nouvelles" (short stories).
I too thought on similar lines. In fact, "books on history" is, in my opinion, preferable to "books about history". However, DL persistently marks such translation incorrect.
"Historical books" suggests old books (on any topic) rather than history books, (books about history).
Well this is long standing problem. I wrote 'on history' instead of about history; this is EXACTLY the same thing in the standard English in England that I speak. What's the point of these comments if they take no notice?
DL seem to have a problem with 'de' or d' in this case. If you click on the translations for de, you are presneted with 'of, from, to' which in many cases is irrelevant. In this case it doesn't like 'on' history, it only accepts 'about' history. You could argue the difference but you'd lose the will to live!
All expressions of quantity including "de" drop the indefinite or partitive article:
- Un peu de / peu de / autant de / moins de / plus de / beaucoup de... livres / bière