As alluded to in the article (although not by name), the
Trivers-Willard Hypothesis has been around since at least 1973.
The logic is simple.
Males are higher in reproductive variance; females are lower in reproductive variance.
Reproductively fit males can produce a high number of spawn, but reproductively unfit males have a large chance of dying childless.
On the other hand, basically every female is guaranteed to reproduce (after all, no matter how ugly, some enterprising male will deign to dump a fuck in them), but the upside is limited by the fact that gestation take 9 months on average, for humans.
From the Dawkinsian selfish gene perspective, if you are resource-rich/reproductively fit, you want sons to heighten the upside. If you are resource-poor/reproductively unfit, you want daughters to limit the downside.
For humans, this is also related to the fact that additional resources from the parent can help men gain status and thus an edge in the sexual market, but not women.
To analogize to finance: Sons are like equity (unlimited upside, but potential loss of entire principal). Daughters are like debt (limited upside, but downside is floored by the recovery rate).
Why Beautiful People Have More Daughters posits a corollary: that good-looking people have more daughters because daughters can better leverage looks in the sexual market.
Although the idea is not new, it's always great to find additional empirical support for old ideas.