Chapter 1: The Secret History (Unrecorded History: Voice of the Angel) of the new World of Darkness core book tells a story about a god-machine, angels, ancients, their children and whatnot.
How does this part relate to the "core themes" (mages, vampires, werewolves, etc) of nWoD? Is it just flavor text, "mysterious/mad rambling", or is this a "backbone" for the whole game world, with clues to be found here and there? If so, what are these clues and which books contain them?
In the first edition of the New World of Darkness, the presence of the God Machine was subtly hinted at in the other core books.
Danse Macabre, a sourcebook for Vampire: The Requiem, details a mini-Covenant called the Holy Engineers, who receive transmissions from the God Machine that they strive to interpret. The intended effect is "oracles in reverse" — they'll receive answers and missions to undertake with the goal of figuring out the question or inciting incidents.
Imperial Mysteries, the archmastery book for Mage: The Awakening, says this:
The following contains spoilers for "These Mortal Engines" in the Promethean: the Created sourcebook, Saturnine Night.
In Demon: the Descent and the second edition New World of Darkness games, the God Machine takes on a much greater significance.
In Demon: the Descent, the God Machine and its angels are the primary antagonist group for the Unchained, who themselves once served the God Machine as agents before Falling and going rogue in pursuit of their own personal Paradises or Hells.
In The God Machine Chronicle, which is an interim book standing in for the forthcoming World of Darkness Second Edition, the God Machine serves as the driver for an entire set of adventures involving the secret demiurge of the world.
In Vampire: The Requiem Second Edition, the God Machine is given as one possible cause for the anticovenant known as VII.