No, it is a new game. The developers are pretending the previous three games (New Nightmare, AitD 2 and 3) never happened so this is a sequel to the first AitD. So far what we know is that in the 1920's Edward Carnby somehow looses consciousness and when he wakes up he finds himself in present day New York, no explanation has been given as to why, but I guess that's part of the plot.
My ultimate goal as a socialist revolutionary was to have my face plastered on the t-shirts of rich white kids. --Che Guevara