Why do we call quantum physics an ab initio model?
Because we can use it to study the large natural phenomena while the quantum physics itself cannot be described more fundamental concepts.
Why do we call classical mechanics an ab initio model?
Because at the level of the natural phenomena that we describe using classical mechanics the theory itself cannot be described through more fundamental concepts.
Is classical electromagnetism an an ab initio model (and if it is one, what are its first principles)?
I dont think so. Because it is used to describe the motion of electrons while the theory itself can be described using fundamental concepts such as quantum mechanics.