Yay, my favorite topic!
"Would this entail a social constructionis basis of gender identity?"
As Douglas Hofstadter would say, MU.
I tend to agree with Dr. Noe, but I think his criticism of Crick is a little over-harsh. His criticism should be of overreaching on the implications of science -- something that philiosophers are notorious for, though many well-known scientists are also guilty of it.
Hofstadter said much the same thing in GEB-EGB 30 years ago: in essence, meaning emerges from interactions between different levels of "reduction" or (conversely) "chunking" of a system. Every theory we have in science (physical or social) is an effective theory that averages the effects of a more fundamental theory in order to illuminate emergent properties. My guess would be that consiousness emerges from an enormous amount of violation of levels of desription, so that neither a reductionist nor a holist description can ever be found (not to say that attempts at understanding are worthless; they are just limited in what they can achieve).
So gender, like everything else, could be described (to give some simplistic examples) psychologically (how an individual feels and interacts with others), physically (variations in brain structures), socially (how society sees individuals), chemically (intrauterine hormone levels), or in a nunmber of other ways. Why not? But no description can ever be complete. When we emphasize one and say "well, gender is really just _____," we are fooling ourselves, whether we fill in the blank with chromosomes or social constructions or something in between.
Gender is not "really just" anything; nor is anything else that is worth discussing.
~Alyssa