Is Ryuk required to write Misa's name in his Death Note at the end of her life?
That rule is an expansion on the rules which state cases when Gods of Death are allowed to return to their own world (more specifically it's the second part of "How to Use: LXIV")

Point one of those rules start with:


  The following situations are the cases where a god of death that has brought the Death Note into the human world is allowed to return to the world of gods of death


While it is true that at one point Ryuk had ownership over Misa's Death Note he wasn't the one who brought it to the human world, so in Misa's case those rules don't apply to him.