Meh... it's a linear story, side-missions don't make sense.
You can have both a linear main story and standalone side-missions. That's what other open-world games do, along with every RPG ever made. In the context of Mafia, the side-missions could be random tasks that your boss provides. There are several cinematic montages that show these random tasks. I don't see why they couldn't be turned into actual missions, especially given the game's lengthy development cycle.
Don't get me wrong, I enjoyed Mafia 2. However, the lack of side-missions is still disappointing.