I have two dogs who are brothers, they've been together since birth. So, they've had the same environment. One is the "alpha" dog, the other not. They're as different as night and day.
That doesn't mean the differences are genetic...we can grow up in the same household but have a totally different experience.
It was actually an interesting study--IIRC it sparked a conflict between the author and another scientist which led to them bickering back and forth over several issues of the journal. The study author theorized the trend is due to anti-male antibodies produced by the mother with repetive pregnancies with a boy (the theory mentioned in the article). The other scientist said that it was probably an environmental effect, perhaps due to a higher likelihood of physical or sexual abuse by an older brother as there were more of them.
It couldn't be genetic in this case, of course, since there's no mechanism to transmit certain genes to a son only when one has produced multiple sons already.