In the video-game Batman: Arkham City, Talia al Ghul and Bruce Wayne's conversations make no mention of their son. Is the game set before, after or on an entirely separate timeline to Damian's birth?
Arkham City is a completely different timeline than the current DCnU. It also does not fall within the canon Post-Crisis worlds established including Zero Hour or Flashpoint. It is a completely separate timeline from any active DC Universe. This does not mean it could not be assigned to one of the 52 universes currently available to the DCnU.
Paul Dini, a writer of the Animated Series has written a self-contained series of stories to contain this particular universe. The stories appeared in May of 2011.
Batman: Arkham City' Comic Book Miniseries Bridges Games
Batman: Arkham City picks up one year after the original game, where former Arkham Warden turned newly elected Mayor of Gotham City Quincy Sharp has decided to close down the infamous institution. In its stead, he establishes Arkham City, the new maximum security home for all of Gotham City's thugs, gangsters and criminals. Inmates can roam free and do whatever they want as long as they don't try to escape. To run this urban prison, Sharp has appointed Dr. Hugo Strange, a man who knows that Bruce Wayne is Batman.