This is supposed to be a remake of the first game complete with many of the same levels. However the story plays out as if Daniel has been in in this situation for some time. For example he and other characters are already familiar with each other, and the developers expect the player to have played Painkiller 1 to even know who those characters are because the remake never bothers to explain.
I haven't played it yet, but I have a question I have sought the answer to for some time and I hope you can answer it. Does Lucifer appear in the game at any point, either in a cutscene, as a boss or both? --- Of all the gin joints in all the towns in all the world, she walks into mine - Humphrey Bogart - Casablanca