Dick Grayson is now Batman because the last time we saw Bruce Wayne was in Final Crisis where he seemingly died from the Omega Sanction shot from the eyes of the evil god Darkseid. The last page showed Wayne was actually alive but in the distant past, still in his Batman garb, laying his utility belt upon Anthro's (who was given the gift of fire at the dawn of human civilization) body and drawing a bat symbol on a cave wall.
From ign.com:
Each of the stories is a twist on a different "pulp hero" genre — so there's the caveman story, the witchhunter/Puritan adventurer thing, the pirate Batman, the cowboy, the P.I. — as a nod toward those mad old 1950s comics with Caveman Batman and Viking Batman adventures. It's Bruce Wayne's ultimate challenge — Batman vs. history itself!
I knew they weren't going to keep him in the past forever, but he's only been gone for a year. What's the rush?