I believe she is referring to Graff as the king who forgets the dream. Graff took Ender from his family to make him into a heroic commander that would save mankind by shaping the good Ender into an aggressive, violentone. She knows this and so does Graff. Graff's advisors and game programmer are supposed to interpret the Giant Game that Ender is playing as to his readiness to proceed up the chain of command. They are stumped when Ender keeps seeing his older brother Peter's face in the mirror instead of his own reflection. This part of the game keeps Ender from finishing.
Valentine is the prophet here. She wants the IF to know that they will take the good child Ender and make him into the twisted, evil Peter who likes to hurt people and animals, who wants to rule the world. By pressuring Val into writing a letter to Ender (who will actually be allowed to get and read this one) reassuring him that he will not be like Peter ever. Her loving message allows Ender to successfully complete the End of the World game, even though both she and her younger brother know the message is contrived. Ender's communication with the only person who loves him solves the game with an act of love. His success will lead him to become the youngest commander ever.