Superheroes are an obvious point of reference for Moffat's run in Doctor Who, not only in his approach to the character ("I mean, life's not a comic book, right, Doctor?" D: "Possibly I'm not the right person to ask"), but in the constitution of his Doctor Who's Universe - which Moffat must have rebooted more times than the Marvel Universe has been in the last couple of years (which are unpopular decisions, I understand, acting against the integrity and continuity of the universe, but, as a comics fan, possible of forgiveness if they are, in some way, good stories).

(I mean, Doctor Who naturally shares an ontology with comics, as a character that persists as its writers change and, as so, must have a flexible characterization, but this would be another digression.)

Getting a superhero in an episode, though, is not only an unavoidable homage. Moffat is constantly playing with doubles: in the essence of The Doctor there is a depth, an indissoluble melancholy that is never made text by the character. He is a tragic character that is never defined by it's tragedy, but, rather, by anything but. Therefore, this essence is consistently approached by indirect means, via characters that reveal their likeness to the Doctor and having them receive our sympathy as he saves his feelings for himself.

In this special, the superhero - as a concept - is a double of The Doctor, one of it's defining qualities. As it is being a Doctor, the man whose name gave our word 'doctor' all of it's meaning. This information, given by the Doctor to a young Grant, is something that is first revealed - and it's noted that a 'double' is also a repetition - by River Song, who's absence is, in this special, at the center of The Doctor's melancholy. Although The Doctor won't make much of a note of her ("What was her name?" D: "I'm sure that I must be busy, I better go", and also Nardone: "But, oh, look at you, avoiding the subject!"), is in referencing such little things that he reveals where his heart currently is.

The Ghost is a riff on Superman, down to a reporter love interest, in a city that has a building with a gyrating planet on top. There's even a reference to Siegel and Shuster. The Doctor discovering the double identity of Clark Kent is actually one of the best scenes

("Take a look at that picture. Now this one. Take a good, long look. It takes a moment to see it. Superman and Clark Kent are one and the same person."
- Are you serious?
"Yeah. Look, I drew specs on Superman."
- Everyone knows they're the same person.
"Well, Lois Lane doesn't. And she's a reporter.")

He leads a double life (as any superhero): the kind and shy boy harboring love for a high school crush, and the hero. The Ghost's arc is the resolution of a simple decision: to stop being a hero and accepting actualizing this love.

The Doctor arc, at this point, is the exact opposite: after losing Clara - to whom he sacrificed millions of years and iterations to punch open a diamond wall, a colossal effort anchored at the Doctor's unshakable resolve (if not his stubbornness), one of his greatest superhero moments -, he lets go of this superhero identity, and embarks on 24 years ("24 years? Yeah, of course it would be that.", also a doubling) of happiness. But this happiness is also melancholic, for his and River's love is doomed -- but so is everything about the Doctor, for even for a Time Lord the time passes and things must come to an end.

The Ghost's arc, so, is The Doctor's absent arc between the last special and this one - which we are not present for, because there must be no happy endings for The Doctor. But, in the nature of the double, there is regeneration, the circularity of time. As The Doctor himself says: "Everything ends. And it's always sad. But everything begins again too, and that's always happy."

Protected, now, by the company of a cyborg - to avoid the hurt of human contact, as is his nature post-heartbreak (see: the Ninth Doctor, until Rose), but also a somewhat memory of River Song -, The Doctor is finally ready to return to be a superhero ("The world will be fine. I've been away for a while, but I'm back.") Which is why, even though The Ghost is a superhero, is The Doctor who (heh) saves the day (I mean, credit where credit is due: The Ghost does holds the ship up, but the Doctor is the one to dismantle Harmony Shoals's plan), even echoing (doubling) the Eleventh Doctor's repeal of the Atraxi ("Who are you? There have been many attempts to conquer the Earth. I've lost count. Not one of them has succeeded, not a single one.They all lost and burned and ran. That's who I am.") another defining moment, by Moffat, of The-Doctor-as-superhero. Which is why this ends with The Doctor's clear cut superhero actualization, as Doctor Mysterio - and everything is ready to begin again.

...

"Why did they call him Spider-Man? Don't they like him?"
-He was bitten by a radioactive spider, and guess what happened?
"Radiation poisoning, I should think."
-No, he got special powers.
"What, vomiting, hair loss and death? Fat lot of use."