So how many heal spells and lightning bolts from fingertips would make this better fantasy?
None.
It doesn't matter how many fantasy tokens the story contains; what matters is what use they are put to. Compare this to "Superhero Girl" - that story had nothing in it that was obviously fantasy, and everything that could have been fantasy had a non-fantasy explanation. But, this ambiguity - whether or not it is fantasy - was at the heart of the story. This story is full to the brim of obviously fantastic creatures, but, for me at least, it didn't feel like this was anything more than window dressing. Yeah, sure, the tree spirit on the boat would not have been possible in a realistic setting, but that was a minor story point, just one of a list of cruelties than were mostly all-too-realistic.
You know how, when little kids play with dolls and action figures, they often create stories that are totally unrelated to the nature of the figures? I remember being around 6 or 7, playing with the girl next door, with my lego figures, her barbie, and my brother's stuffed animals. Sometimes the lego guy and barbie were husband and wife and the purple bunny was their son, once I remember barbie being a doctor and the legos and animals her patients, and so forth. The stories we acted out and the characters acting them out were not particularly related to each other. That's sort of the vibe I got from this story. "Centaur" and "sphinx" were just random character traits. The only species that realy mattered was the humans, since this was a story about human cruelty.
To make this better fantasy, it doesn't matter how many fantasy elements are added, what would need to be added is a non-cosmetic function for them in the story. As has been pointed out several time in this thread, the same author, in the same (or very similar) setting, has succeeded in doing exactly that in the story "'I'll Gnaw Your Bones' said the manticore" (or whatever the accurate title was, I'm typing this from memory). Here, in my opinion at least, she failed at doing so.