I'm really not an expert, but I'll try to weigh in anyway since I consider myself non-binary. I would not call myself "genderqueer", for a couple of reasons.
Genderqueer: Describes anyone whose gender identity is non-normative.
Nonbinary: Describes anyone whose gender identity does not conform to the gender binary.
Which are identical, as far as I'm concerned. "Non-normative" is "anything that is outside the norm", which then just leads to "outside the gender binary", which leads directly to "nonbinary". They are functionally identical, with the caveat that it is by these definitions. A different set of definitions would likely yield different results.
This may sound absurd, but I don't accept the idea that there's anything normative about the supposed gender binary. Very few people fit fully within the stereotype of any gender, almost everyone has both male and female aspects. I believe the definition of "genderqueer" you provided could be applied to almost everyone, or maybe no-one, but it'd be very tricky to apply it to people on a case-by-case basis.
Fortunately it's not a label you apply to people, but one which people adopt for themselves. If they *feel* like their gender identity isn't "normal", that makes them "genderqueer".
I've felt that way in the past but I've decided I don't feel abnormal, so the word isn't for me. I'm also a bit uncomfortable describing myself as queer in any way. It's a reclaimed slur and while I don't mind anyone using it, I have bad memories of it.
Your definition of non-binary seems alright, except that it's also a term that people choose. An androgynous man can't be declared NB just for not conforming to his gender. Typically someone is NB because they don't strive to be either gender of the binary, that's all. Some might additionally be uncomfortable being considered a man or woman, though that's not required. Some enbies are happy with any pronouns, others prefer neutral language or personal pronouns.
There's a related concept, gender-fluidity. These are people who change gender fairly often, usually at the start of the day. Often this is done within the gender binary, though not necessarily. So someone can be genderfluid, NB, both, or neither.
Okay I hope that was at least somewhat accurate and maybe even helpful!