a vast majority of all healthcare systems support just the simple genders male, female, unknown, and other, or some subset of those. Making the gender a full CodeableConcept is much harder work for anyone reading resources, and only relevant in very few cases. Hence, implementers can provide an extension (to clarify the meaning of 'other', usually).
For the 'the AdministrativeGender element' - are you asking about the ValueSet here? If so, where it used is linked from that page. Otherwise, what are you referring to?