Kirk, McCoy, Uhura, and others have their genders swapped, while Spock gets an extra Y chromosome, making him extra aggressive. The same has happened to Kang's ship, with Kang receiving an extra Y chromosome. Spock comments that "it is done only to one male on a ship" to which Kang agrees: "The strongest."
The whole story is just teasing about the now female Kirk potentially having sex with Kang (mostly) or Spock (maybe), and moaning about how being female makes him unfit for command. With all the stylistic suckiness Marshak and Culbreath can bring to bear, too.