I don't think they are assuming everyone else is binary.
He's at least assuming they're not non-binary, because he says he's the first "non-binary priest"!
The only way you can totally reconcile this with no assumptions about other people is if you conclude that non-binary is meaningless, hence not being non-binary is also meaningless.
But I think you can reach a mid-point where non-binary means "someone who wants you to pretend they're not a man or a woman (ostensibly due to odd ideas about sex roles)". In which case, yes, he is the first of those, and it is true that most other people do not want you to pretend they're not a man or a woman, and it may indeed be true that there has not been a CoE priest demanding that before now.
The problem and objection with "non-binary" really comes down to the fact that people are expected to accept believers' own definition, and follow their religious tenets. It's as if we were expected to think of "Christians" as "someone who is going to heaven" rather than "an adherent of Christianity", and also to engage in their rituals.
"Non-binary" makes sense as a religious signifier. The sooner everyone recognises that, and treat it in a secular fashion - so the demands on others stop and it becomes a purely personal thing - the better. (And it's far from unusual for a religion to have regressive ideas about sex roles - it fits in quite well).