"What is a unit? The majority of the devs would probably answer "It’s a class". "

A unit is a unit of behavior, which could be a single function or a flow of work. The pattern of the test defines it.

"His point is that people who do what they call "unit testing" always test the implementation (classes) but not the behavior"

And his assertion is incorrect. It demonstrates a lack of knowledge of unit testing and inexperience working with people who know how.