What does linking my my2K account do?

Solution 1:

From the 2K FAQ:

my2K is a user account system used across a variety of 2K products. Currently, it appears in a handful of our recent mobile games, as well as the official 2K website.

For XCOM 2, linking your my2K account does the following:

Connecting your my2K account to XCOM 2 will eventually allow you to keep track of your in-game statistics.

For Evolve, from here, linking your account does this:

The biggest question we've received is "Why should I connect to my2K?" my2K provides some benefits for players looking to improve their game in Evolve. Not only does it allow the Evolve Game Changer website access to your game info and provide you with detailed analytics on your gameplay, it also lets you connect to the Hunters Quest mobile app. Hunters Quest lets players unlock exclusive and speeds up the character mastery progress.

Based on the way it interacts with the aforementioned games, linking your account in Mafia 3 will most likely track your in-game statistics so that you can view them.