> Our results also have important implications for mechanisms underpinning two major language dispersals. The expansion of the Indo-European language family from the Western Eurasia steppes has traditionally been associated with mounted pastoralism, with the CWC serving as a major stepping stone in Europe39,40,41. However, while there is overwhelming lexical evidence for horse domestication, horse-drawn chariots and derived mythologies in the Indo-Iranian branch of the Indo-European family, the linguistic indications of horse-keeping practices at the deeper Proto-Indo-European level are in fact ambiguous. The limited presence of horses in CWC assemblages43 and the local genetic makeup of CWC specimens reject scenarios in which horses were the primary driving force behind the initial spread of Indo-European languages in Europe44.

This is a pretty big shift in the story of how the IE languages spread westward to Europe. It also would seem to firm up the timing of the spread as happening sometime not too much later than 4000BCE (when horses were domesticated) since the westward spreading peoples had horses, but horse culture hadn't become as central to their lives as it was with the eastern-migrating IE speakers.

> By contrast, DOM2 dispersal in Asia during the early-to-mid second millennium BC was concurrent with the spread of chariotry and Indo-Iranian languages, whose earliest speakers are linked to populations that directly preceded the Sintashta culture11,12,45. We thus conclude that the new package of chariotry and improved breed of horses, including chestnut coat colouration documented both linguistically (Supplementary Discussion) and genetically (Extended Data Fig. 8)

I can't see the Supplementary discussion, but the chestnut coloration is likely referring in part to the Vedic (1500BC) description of a red horse (aruṣa). There are also probably contemporaneous Avestan terms.

It's pretty neat that the early mention of a chestnut/red colored horse parallels the genetic distribution of that phenotype, if I'm understanding the article correctly.