I'm writing a story that involves monsters, magical creatures, that sort of thing, and there are some monsters, like wendigo as an obvious example, that can only sustain themselves on a diet of human beings, whether their flesh, their soul, their brains, whatever. Now, we have scientific terms that categorize creatures by what they eat, most notably carnivore, herbivore, and omnivore. If we follow the same rules of language that spawned these words, what would the proper term be for a creature that eats humans?
Possibly just "man-eating". There's been lots of research into animals that sometimes prey on humans e.g. due to stress, and the articles about that just call it "man-eating". Certainly Wendigos etc would be "specialist predators". Anthropophage is solid but bear in mind:- "Anthropophagy" in science and in popular use most often refers to cannibalism not animals preying on humans "Anthropophage" can refer to a specific monster (see https://en.wikipedia.org/wiki/Anthropophage) There is "Cordylobia anthropophaga" which is a blow-fly that eats human hosts - but so do lots of things and it seems to be a rare term in Latin names They don't seem to use this word for man-eating lions. English words with -phage or -phagia on the end usually have a strongly unpleasant connotation Anthropovore I like less, because there are lots of creatures that specialise to eat one species, but they don't usually coin a new term for them ending in -vore. It isn't limited to carnivore, herbivore, omnivore... below that there is nectarivore, insectivore, frugivore, piscivores, rodentivores and many others... but the logic doesn't extend down to a specific species. E.g. kites are rodentivores, but there aren't "rattivores" or "murivores". At a stretch maybe "hominoidivore" - that would be a new term without any baggage from existing science, and general enough to fit with the logic. Another alternative might be to establish a term that sounds right for the story - by basing it on popular slang or the name of a scientist.
I'd call it an obligate carnivore with a preference for humans rather than try and get fancy with specialized Latin terms. Animals that eat mainly one type of prey (polar bears and seals, lynx and snowshoe rabbits, for example) are capable of eating other prey and do eat other prey if it is available.
I don't see what's wrong with man-eater, and if it's a fantasy setting you may not want to use scientific names either. But if you really wanted, another option among others already suggested would be 'Primavore' (pronounced like prima donna) but that would imply they feed on other primates too. Bonus points if the humans are arrogant and take the 'prima' (first) to heart.