A non-binary person does not identify as no gender, they identify as a gender which does not fit into the binary categorization that society has -- i.e. man and woman, they do not see themselves as one of these two.

So if they are assigned a man, and do not identify as a man.... Define transgender...

" A transgender person (often abbreviated to trans person) is someone whose gender identity or gender expression does not correspond with their sex assigned at birth."

So their gender expression does not correlate with man, for example, which they were assigned at birth because they are male... Thus they are transgender. As I said, this doesn't make a non-binary a transgender woman, but it does make them transgender because their gender identity does not align with the gender they were assigned by the social roles of their sex.

I hope that makes sense... You're free to disagree, but that's it -- the gender binary and not being attached to that is irrelevant to whether or not they identify as a different gender to what was assigned to them, as would be the case if they identify as a gender which is not usually assigned at all.