“Why do we call quantum physics an ab initio model? Why do we call classical mechanics an ab initio model? Is classical electromagnetism an an ab initio model (and if it is one, what are its first principles)?”
I think that QM is a ab initio model because it serves as the building blocks for atomic and molecular theory. These concepts in QM are the most fundamental, from which the atom is the build up.
Classical Mechanics descibribes the motion of objects and such. It provides some fundamentals from which the motion of the objects in question can be described.
Electromagnetic theory is also an ab initio model, it uses the maxwell equations as its fundamentals.