From the wiki quote you provided I’d have to disagree. From what I can see here the nomenclature goes like this:
Higher primates = Simians.
Simians = Old world monkeys + (apes+humans) + new world monkeys.
Then, Simians - new world monkeys (went to south america) = catarrhines
catarrhines- Old world monkeys - (apes+humans) = 0 (the state of the world today)
Now, maybe I’m still wrong (happens all the time), but that’s what this wiki excerpt says, I believe
Regardless, if the entity in questions does indeed self-identify as an otherkin, and does self-identify as a ‘monkey’ then I’m deeply sorry should I have offended the entity in question.