Mafia is still about the Italian mafia in the U.S. The enemy faction is the Italian mafia. One of the friendly factions is also Italian mafia. Mafia 3 just added the black mafia and Irish mafia to the mix because it made sense within the game's time period and location.
As I said before, the series went in a completely different direction. The lead writer of the first two games left to create a new studio and took most of Mafia's original staff with him. I'll eventually get part 3 on sale since it looks pretty awesome in its own right, but I really wanted a true sequel made by the original team.