If you're looking for something that's designed for programmers and feels less like canned game maker software, then I think you would like the C4 Engine. It's entirely based on C++, it's aimed toward FPS games, and it runs on PC, Mac, and Linux. The only one of your criteria it doesn't satisfy is that it's not free, but you get lifetime updates after purchasing a license.

http://www.terathon....ne/features.php