Darrow wins because he stops accepting the Institute as a closed system. The Proctors expect him to fight other students while they control the conditions above them. His attack on Olympus makes the hidden level of power visible and turns the school's own technology against it. It is the novel's clearest model of revolution: do not merely outperform opponents inside a rigged structure; identify who maintains the structure.
Mustang's identity gives that victory its final uncertainty. She is not simply a gifted ally but Nero's daughter and the Jackal's sister. By delivering Adrius, she proves that family does not completely determine loyalty. Darrow's silence about being Red means their trust is still unequal, however, and the revelation will eventually test everything built in the Northwoods.
Accepting Nero's offer is both strategic triumph and moral danger. Darrow gains access to the center of Martian power, exactly as the Sons intended. He must now serve the man responsible for Eo's death, benefit from Gold status, and maintain relationships that are real even though his identity is false. The Institute trained him to rule; the next question is whether infiltration can destroy that training before it remakes him again.