The Mad City is part of the Dreamlands described in the Cthulhu Mythos.
Mother When is one Avatar of Nyarlathotep that just pass to be more active in the Dreamlands. Just For the Evulz, as usual, he/she/it created the Mad City and manipulates regular people to enter portals to the Dreamlands (The Doors), giving also Madness Powers to them just to make things more amusing. The Madness powers work and can manipulate reality because the more insane you become, the more open your mind becomes to the reality of the Mythos, until all that's left of you is a minion unable to get out the Dreamlands. Of course, you also can get out and Awake, but you can't enjoy normal life because a part of you knows the world is bigger than that. Even if you Awake you lose because you can only escape because Nyarly would get bored if he always win. About the 13th Hour, as Incarnation of the Will of the Outer Gods, he has some limited control over the powers of Yog-Sothoth that allow him/her/it to manipulate space and time. The City Slumbering is another layer of illusion.
The narrative has some curious wording - while the Mad City is written like a global phenomenon, it has a very specific layout and is mapped on the Slumbering and its districts, as if it was the only city in existence, and fluff text avoids acknowledging any world beyond the Slumbering too. This brings in mind the City from Matrix, and a question: what is the real world like then?