It's a retelling but arguably the elements are there.
Khan wants revenge, but this time not against Kirk, but against Admiral Marcus who essentially enslaved him. This time you can kind of see his point. In TWOK the potentially dangerous weapon is not Genesis but Khan himself (and I suppose his superblood, and maybe the Vengeance). There's the element of an an officer dying to save his ship, but it's Kirk instead of Spock. We even get the Khan scream, though it's not.. as.. good. Oh yeah, and Carol Marcus, albeit British Carol Marcus, who is the scientist child of an Admiral, so we don't need David. Well, maybe there will be a David way down the line, who knows.