|Later, the winged tiger got hungry|
One of the best things about authors is that they are a creative lot, coming up with fascinating things and ways to twist the familiar and known into a unique, clever story. This creativity drives the fiction process, because even books set in or written around real events require creative thought to flesh out the events and characters beyond what is known historically.
This creativity means that people will come up with all manner of variants, twists, and changes in basic concepts, which is a good thing. From its earliest roots in legends of gods and fairy tales to the writings of men like Dunsany and Tolkien, fantasy writing followed a pretty standard set of ideas. You had lands of legend with heroes and fantastic creatures. Magic was a part of the equation, whether the power of the squabbling gods or wizards.
C.S. Lewis and J.R.R. Tolkien created the first true fantasy stories out of myths and fairy tales, establishing standards in races and concepts that have endured ever since.
As time went on, fantasy expanded. Michael Moorcock created brand new worlds and concepts, Roger Zelazny, Fritz Lieber, Robert Howard, and others shaped the idea of fantasy into a version called Swords and Sorcery. Urban Fantasy, Science Fantasy (such as Star Wars), and other sorts began to develop. Books began to be labeled as some sub-category of fantasy for having the slightest trimmings of the fantastic. Is Interview with the Vampire fantasy? A Song of Fire And Ice? Twilight?
And eventually the definition of fantasy kept being stretched and redefined and re-imagined until its lost almost all meaning as a category. So what does fantasy even mean? How is fantasy to be defined at all, after all these changes? Or is there even a category of fantasy any more?
For me, fantasy has to be more than simply a setting with fantastic elements. Peter Pan and Fern Gully are fantastical in setting, but are they fantasy? The Dragonriders of Pern series has plenty of Dragons and medieval-feeling culture, but is it fantasy? Certainly these works have fantastic things in them but fantasy has to be more than oddity and creativity.
Fantasy has to have magic in it. That's the basic definition to me. If there's no magic, then its just an interesting, possibly space opera or fairy tale setting. But no magic, no fantasy. This magic doesn't have to take the form of wizards flinging lightning bolts, it can be more subtle, however. It comes down to how things are explained and why they work.
The Dragonriders of Pern books are science fiction, even if its in the fantasy section of your bookstore or library. The dragons are genetically engineered animals that were given their abilities by science. Their abilities, their origin, and even their purpose is all science fiction. The fact that they look like and are called dragons doesn't make them fantasy because there's nothing magical about these creatures.
But if these dragons were mystical creatures that flew and breathed fire naturally, were their own creatures instead of genetically manipulated lizards, and used magic to jump between locations, that would make it fantasy.
Because its the unknown, the magical, and the mystical that makes things fantasy. If you explain everything through scientific terms and careful analysis, it stops being magical, and hence stops being fantasy.
Fantasy books don't have to have monsters - in fact, in my second fantasy novel, the monsters are all human. But the magic has to be there. There's no need for elves, heroic knights, forests and castles (although they all help). But if you leave off the magic, its no longer fantasy and its just an alternate world history, such as most of the Game of Thrones storyline.
Your interpetation may vary, but for me: no magic, no fantasy. And if you expand the definition so broadly that includes anything, fantasy means nothing. Without that minimum, baseline, there's no real category at all of fantasy.