What is symbolized in Gabe's comment "I own you," in Act 1, Scene 8? What is revealed in this scene regarding his character?

Gabe says, "I own you," indicating that he is alive not only to Diana, but in other ways to Dan and Natalie too. Natalie leaves Dan and goes to the bathroom, where she takes a couple of Diana's pills, Gabe singing that he is "behind" her. Meanwhile, Dr. Madden suggests that because Gabe would have been eighteen, it's time for Diana to let him go.