That’s actually wrong.
“Intersex” is a general term used for a variety of conditions in which a person is born with a reproductive or sexual anatomy that doesn’t seem to fit the typical definitions of female or male." (ISNA) Intersex people can identify as binary.
Agender is one form of being non-binary. There’s a lot of others. It’s also not a term I’d tend to use in a fantasy game.
As has already been said, cisgender is just the opposite of transgender. Most people are cisgender, Non-binary comes under the transgender label.
I’d admittedly not use any of our terms for describing gender and sexuality in a fantasy game. I think in this case making up your own terminology, using it to slot into your own world, is perfectly acceptable. It may involve a little bit of world-building, just working out how it fits though, how people see things.
I don’t particularly like changeling, but that’s because it’s a word I tend to associate with a child that’s been stolen away by the fae and an impostor left in its place.
Have a read of this thread, particularly the posts after the one I just linked to. Writing Non-binary MCs - Noble Nouns & Other Questions - #21 by SwanMaiden