I wondered if the line about the Kings, may be a slight red herring in the way it's used in the trailer.
It's Vickers that says it right? Isn't she a Weyland Suit?
Could it be that she is referring to Weyland's reign as CEO of the company. Weyland is determined to be part of the mission and the timeline clearly indicates that he harbours ambitions to cheat death/ create life (possibly his own).
Vickers herself may hold ambitions with the corporation and believes that Weyland's time will come eventually.
Obviously the line has greater symbolic resonance thematically, but it could just be that this line happens in a scene where other crew members (maybe Janek) are discussing Weyland and his presence on the mission.