How are the number puzzle pieces defined as frame numbers?
These numbers correspond to animation frames, which in turn, can be seen in Blender. They are passed to a procedure call on each step. The procedure takes them as parameters and plays the animation. You can setup which parameters will be passed in a procedure using the gear icon.
In fact, this particular example was created by a programmer hand. An artist would just put all the steps in a long chain of puzzles – this is bulky yet clearer for understanding.