As well as PS3 and PS Vita
When a new console comes out and there's nothing left to play, we sometimes resort to buying games we'd otherwise never get. Thinking back to some of the utter garbage I bought on Xbox Live Arcade in the Xbox 360's first year sends me to a sad place indeed. Desperate times. Now, I'm not necessarily saying Backgammon Blitz will be one of those titles for you, but it might be.
The game will be out later this winter for PS3, PS4, and PS Vita and it's coming from VooFoo Studios, the team responsible for Hustle Kings and Pure Chess. I'm sure they'll be able to do Backgammon just fine. The PlayStation Blog has a couple of screenshots and also says that Blitz has asynchronous cross-platform play, so that's something.
Backgammon Blitz Coming to PS4, PS3, and PS Vita This Winter [PlayStation Blog]