I have never played another FPS that had a mode like this, and it was so damn fun and self-balancing.

Having said that, I don’t have the time to game nearly as much as I once did, so I have missed plenty of modern titles, even big ones.

Is there anything still being played that has a mode like this?

From the link, emphasis added:

Nash Werner of GamePro said of the PC version, "With its well-written storyline and thought-provoking missions, SoF’s singleplayer will keep you thrilled for hours, and you’ll probably be playing the Assassin mode for months.

Edited to describe it: (from memory)

In this mode, it’s a lot like Deathmatch mode, except each player is assigned a target. You can only shoot your target or the person who is targeting you. You advance up the rankings by killing your target.

The genius of the mode is that the more you are dominating, the more people will respawn with you as their assigned target. So pro player on the server is going to have essentially every other person on the server trying to kill just them very quickly, while a noob is never going to be targeted by more than one person. If you are having a day where you’ve really hit your A game, it’s very, very satisfying, but it’s still fun if you aren’t having a great session.

This is happening dynamically throughout the match as people respawn, so it’s very fluid, and the balance shifts during the game continuously to keep it fun for everyone.