I actually have read the book, and the book doesn't say or even imply that cats think of us as cats.

Please note that I did not mean to imply cats do not know us from them.

Fair. But there is a lot of nonsense around that subject on the Internet because people misinterpret what it says. Even in the article you linked, they ask that question and he corrects them.

In the book [I say] that cats behave toward us in a way that's indistinguishable from [how] they would act toward other cats.

Specifically that. Because dogs operate in unit groups and they recognize a hierarchy. Cats, even in social groups do not have a hierarchy and treat us as members of their colony. They socialize with us as such, but in an equal but different capacity. That's misinterpreted a lot.

I apologize for assuming that was the point you were trying to make.