How can I reproduce the MatchMoving/MotionTracking technique from Just Dance? I'm a software engineer student with a big projet idea but low graphic knowledge.

My goal is to compare two people dancing. One person would be the teacher with perfect moves and the other would be a dance trainee.

From my beginner point of view, all I need to retrieve is both skeletons with a motion tracking camera (like Kinect?) then I can do maths with the different reference points (X,Y,Z).

Is there a motion tracking camera + API or Library you would recommand me ?

I do not want to open a 3D software like MeshLab. I would like to retrieve the reference points through line of codes and manipulate them as I wish.
The Kinect SDK has a skeletal tracking demo in the c++ api (BodyBasics). The skeleton you get is the same "topology" unless it fails to acquire the skeleton. So you can easily compare the left shoulder of two captures as you always know which point it is.

You'll have to experience with metrics. A simple point to point metric would probably be sufficient though. Maybe with some weights on different body parts though.