That's where you got your definition of trans wrong. The trans label refers to transgender, transsexual and transvestite. If he dresses up as a woman, he's a transvestite, and because he's operating in female gender norms, he's a transgender.
While it may be an "act", it doesn't mean he doesn't think of it as part of himself and his identity. I don't know if he's specified it's not an act, but I don't think you can say something doesn't fit his act. Unless he specifically says he wants to appear like a stereotypical woman, then he can have any type of gender expression in his act.