Going back to the OP:

"The study, which was published in the Royal Society Open Science journal, employed phylogenetic methods to investigate the relationships between population histories and cultural phenomena, such as languages, marriage practices, political institutions, material culture and music."

Phylogenetic: online definition: "relating to the evolutionary development and diversification of a species or group of organisms, or of a particular feature of an organism."

So it looks to me as if they have used a computer programme designed to trace genetics and applied it to bits of stories/themes etc.

So how far the somewhat 'sensational' reporting of this really reflects the claims of the study, I don't know. I know that scientists do sometimes critique/complain about the way scientific findings are presented by journalism. But I'm thinking you would have to mount an argument that methods designed for use in one context might produce meaningful results on another?

Just throwing ideas out here, happy to hear objections/thoughts...