Do I think the author's discussion applies more to the typical families in the US than to families in general

Yes, I do.
Let's just say there's no father in this family. There's only a mother and a boy who has an older sister. In this case, ten to one, the boy thinks he's the man in the family who has to take care of his mother and sister. But also, his siter, who is the first child, thinks she needs to look over his little brother. Therefore, they both are likely to be responsible and capable.
Another .What if the oldest one has some kind of disabilities such as mental disorder? In this case, the second oldest would be the most caring one. The oldest one could also be caring in spite of his/her problem, but it can't be as much as the second oldest is.
This article is based on the premise that siblings are either all male or all female and every member in the family exists and is well, which is apparently not able to be true, always. It does apply to the typical families or at least families that are thought as ordinary by people. And not only the ones in the US, but also everywhere. It just doesn't cover many cases that are possible.