Babylon's streets open Prince of Persia: The Two Thrones, the closing chapter of the Sands trilogy, where the prince shares a body with a darker self. Ubisoft mixed the old acrobatics with speed kills in 2005, letting a stealth kill from a ledge replace a long courtyard fight.
Chariot chases cut through the city between rooftop runs, and the Dark Prince's chain becomes a weapon and a swing line when the transformation hits. Farah is back in the story after the island detour of the previous game.
The cube disc is the original release of that Babylon ending, and a later motion-console build followed the same campaign. Speed kills and the inner voice are the point of this chapter, not a new hourglass tutorial.