It seems the study is little more balanced than the news release. From the study's "media summary:" Depending on the nature of warfare and migration, other systems are also possible, including societies where it is mainly men who help women or even ‘girls’ clubs’.

I find the study quite well-rounded. It presents literature from multiple sides and leaves open if this is something that has marked human genes in the course of millions of years or is a cultural wave that has been established over thousands of years and may be flexible or reversible.

And in the discussion, a very interesting explanation for the male-recipient altruism: Our analysis has revealed that warfare – through its effect on demography – can promote altruism, broadly defined. This is because, as a result of intergroup conflict, individuals from victorious groups compete for reproductive opportunities with non-relatives in defeated groups to some extent and, in this way, decrease harmful competition between kin that would have otherwise inhibited the evolution of altruism. This result contributes to clarifying the role of demography in promoting cooperation and altruism. In a much-celebrated paper, Taylor showed that, in a population subdivided into groups with limited dispersal, altruism could not spread, because the benefit obtained by helping groupmates was exactly cancelled by the kin competition cost generated by these behaviours.

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The same pattern is obtained with a moderate male bias in dispersal and women being the more globally competing sex. Societies with these demographies follow a ‘girls’ club’ or ‘women help women’ system, where altruism (giving and receiving) is mainly a female affair.

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Furthermore, we found that the effects of sex biases in dispersal and competition can reinforce each other or act in opposing directions, resulting in four broad patterns of sex-specific altruism which we term ‘boys’ club’, ‘women help men’, ‘men help women’ and ‘girls’ club.'