He is supposed to be your character from the first game. While in the first game, the player's name is never revealed. There is an FBI Agent who has your picture on a wall in a hotel room and the name says "Trapani The Player". Your character's father who is killed at the beginning is named Johnny Trapani and the bakery that was bombed was taken over by the Straccis.
In this game you play as Dominic, Aldo Trapani's under boss. Aldo is mentioned as Michael's right hand man and the Don of New York. Which is the position you achieve in the first game when you take over all territories.