> science of science is epistemology

That would be the Philosophy of Science.

https://en.wikipedia.org/wiki/Philosophy_of_science

You are not wrong but he's not either. The science of science, or metascience, is a field of epistemology, is a philosophy of science. They are all part of the same thing.

Epistemology is the study of knowledge. If science isn't a form of knowledge, what is?

Science of science is metascience aka meta-research. Applying scientific method to science.

https://en.wikipedia.org/wiki/Metascience

http://metrics.stanford.edu/

Epistemology is philosophy of knowledge, justification, and the rationality of belief. Epistemologists don't use methods that would make it science.

Is the scientific method really being applied here though? Certainly doesn't look like it.