The study suggests that the difference is not genetic, but rather more likely due to differences in parental treatment of the first and subsequent children - that "...older children are showered with attention early in life and treated as leaders in the family. They are handed more responsibility after younger siblings are born and live with higher expectations from their parents." The differences in IQ correlated with the spacing between the children; "children born less than a year apart had the greatest IQ gaps. Differences in IQ scores diminished when there were more than five years between the first and second child." That last point makes some sense to me; when the first child is older, the parents may be less stressed and able to focus more on the second baby than when there are two children in diapers at the same time.
My parents had only two children, my sister and me, and I'm the older one by 19 months and one day. And yes, my IQ is higher, by 3 points. (The story states that an "average" IQ is 100 - I will only say we are both well above that average.) We both believe in the reality of the birth-order effect and have had many discussions about it, in connection with the differences and similarities in both ourselves and her two boys, ages 7 and 4. It's a topic my husband and I have also talked about in relation to his older brother - he's the younger of two boys, 15 months apart - and my stepchildren, ages 12 and 7. (My son's an only child, so he's technically a firstborn, but has no comparison points.)
The study data came from the results of required IQ tests taken by 240,000 men conscripted into the Norwegian army between 1985 and 2004. I think this leaves open the question of whether the results extrapolate to women.
Other considerations are that "smart" encompasses other, less easily quantifiable, qualities besides IQ score, and that "success" can be defined in various ways. But it's always made sense to me that your position in your family of origin would have a pretty strong effect on how you develop and who you turn out to be - it's one of the determinants of how people relate to you, and environment shapes us just as heredity does. (Whether one outweighs the other is not part of this conversation.) It's a topic that fascinates me, and I'm sure my sister, my husband, and I will keep talking about it.
UPDATE 6/25: They're talking about it today over in On Balance.
UPDATE 6/27: An interesting follow-up commentary on today's Huffington Post suggests that birth order doesn't really become a factor until there are at least three children in a family, and even then it may matter less than spacing between the children, gender, and various other factors. Coming from a two-child family, I'm not sure how much I would agree.