Not sure I agree with him. What does something being real mean? It's got to mean that observations are consistent with the description of that something. That's actually all we can do, check that observations aren't disagreeing with what the model said. So if an electron is a tiny little thing that is deflected by a magnetic field, has a certain mass, etc, then it's real insofar as we observe those qualities. In the same way if Santa Claus isn't real, it's because there's issues with the evidence.

This doesn't preclude there being a better model of course. Observations can get more sophisticated, revealing that your model needed adjustment. Or parsimony can drive and someone finds a way to describe multiple phenomena at once, eg electromagnetism.

As for why mathematics is great at describing nature, it's because there's loads of it, since it's an extensible system of logic. Someone somewhere is going to find a way of describing how asteroids go round, and being a kind of logic there's no way you would say it wasn't math, regardless of what exactly it was. Epicycles are math too, despite not being the exact right way to think about it.