A person with XX chromosomes is female--no matter what she "looks" like.
And a person with XY chromosomes, is a male, no matter what he "looks" like.
Providing, of course, we are speaking of genuine X and genuine Y chromosomes, and not some freaky mutated X that has lost a leg through some damage or other, and so looks like a Y.
If a person has, for example, XX chromosomes and yet has what "appears" to be a male sex organ because of some weird mutation or birth defect or other mutilation, then I sure wouldn't blame her for wanting her body to better express her true sex, as determined by her female, XX, chormosomes.
But if someone who is XY and has a pensis--i.e., is a normal male--wants to make his body resemble that of a woman's by having a "surgeon" cut him and stitch him into a different shape--that guy remains a guy and I will refer to him as a he.
Likewise, the XX person is a woman is a woman is a woman.
And should there be something that does not fit either of the two above categories, then it is not male and it is not female: It's a third sex or it's sexless.
Regarding a "functioning penis", I heard not long ago of a male to female to male transexual. Basically he was either disfigured or born with some defect that left his male organs damaged in some form, so a doctor preformed gender reassignment surgery on him when he was an infant and his parents raised him as a female (the doctor, IIRC, wrote a book on the "success" of it all). All his life he never identified well as a female and it wasn't until he was an adult that he discovered what really happened. He since had a second surgery to restore his male appearance to match his identity, complete with pump-action penis (yes, the term makes me snicker too). He has since married, though I don't know (and do doubt) whether he is able to father children of his own. Since his penis is arguably not "fully functional", is he not a man even though he was born male, obtained surgery to reestablish himself as male and intends to live as a male?
I seem to remember the case you're citing as one where the fellow was a victim of a botched circumcision; the doctors then compounded that error by advising the parents that the kid would have emotional problems over his stunted organ, and so would be better-off as a "girl"--he wasn't: he wasn't made a real girl and he wasn't better-off; because he had the male, Y, chromosome.