What does that say, other than: that, in a modern sociological environment, certain genetics-mediated brain differences cause people to behave (react) in different ways to their environment?

It says nothing about what inherently is a mental disease and what is not. Perhaps genetic differences causing certain mental "diseases" in average American society (or whatever society in which you conduct a study) actually benefit the individuals in societies with different cultures or structures. In the same way that certain non-psych heritable "diseases" confer some advantages and disadvantages (sickle-cell anemia and malaria, for instance). Fact is, many genetic differences that some people regard as undesirable are not even classified as diseases, even though they have advantages and disadvantages, if not for lifespan, certainly in social mobility within social environments.

tl;dr: it's patently obvious and beneath discussion that in certain genetic differences might lead two otherwise identical individuals to differ on whether they have different behavior, just as they might differ in many other ways. It's the determination that different behavior in some cases is a "disease" that seems to be at the heart of Szasz's critique of psychology.

How do twin studies rule out "environmental" that is, non-genetic, causes. Twins look alike, so if there are ideas about how people who look alike ought to act alike we would be expect a correlation between genes and behaviour that has nothing to do with the content of the genes. Rather, that behaviour would be motivated by similar ideas.

So thoughts, feelings, and behaviors are outside of biology? How does that work?

I realize that you are simply quoting a passage and not necessarily personally espousing what you wrote.