High fantasy is about elevated tone and questing to affect the destiny of the world, and has nothing to do with the degree of presence of nonhumans and magic.
I'am sorry to contradict you but I have another definition that illustrates well high fantasy:
"… the world of magic, wizards, princes and princesses, dragons, goblins and talismans, jewels, duels and enchantments, the battle between good and evil fought by heroic warriors, common folk and dark monsters."
Here another more precise definition:
"High fantasy is a subgenre of fantasy fiction that is set in invented or parallel worlds. These stories are serious in tone, often epic in scope, dealing with themes of grand struggle against supernatural evil forces.
Other typical characteristics of high fantasy include fantastical races (such as elves and dwarves
), magic, wizards, invented languages, coming-of-age themes, and multi-volume narratives.
In some high fantasy, a contemporary, "real-world" character is placed in the invented world. Purists might not consider this to be "true" high fantasy".
On the other hand, Sword and Sorcery is:
"a fantasy sub-genre featuring muscular heroes in violent conflict with a variety of villains, chiefly wizards, witches, evil spirits, and other creatures whose powers are—unlike the hero’s—supernatural in origin. The term was suggested by Fritz Leiber to Michael Moorcock in 1961."