From SA Mafia Wiki
Ecco defines a "traditional" mafia game as having the following essential elements: 1) an uninformed majority who 2) seeks to remove 3) an informed minority, who in turn 4) seeks to dominate the uninformed majority. Ecco considers that to be the basis of the game of mafia in its most fundamental form. It's what separates it from other games, like the game where everyone was a Serial Killer; it may have been a lot of fun, but it was not "mafia," because it lacked the elements of mafia. And the game of "Paranoia" - it was incredibly difficult to turn that into a "mafia" game because the two are fundamentally different games with different elements.
This has the implication that when a game is called "traditional," Ecco expects it to have the four elements: an uninformed majority... seeking to destroy an informed minority; an informed minority... seeking to destroy an uninformed majority. Things can be added on top of that: roles, flavor, third parties, and so forth. But if the fundamental focus of the game is not the conflict between the majority and the minority, then it's not a traditional game of mafia, if it's even mafia at all.