There seems to be a disconnect here. The original paper says something else, but the reporter writing in Science (today's print issue) draws a somewhat different conclusion. Quotes Priya Moorjani again though not sure if the conclusion is hers. Still, I don't know how language and genetics are mixed up in this paper. Bolded for emphasis by me.
This is the conclusion (last paragraph of the discussion section) in the original Willerslev paper:
"Thus, while the Steppe Hypothesis, in the light of ancient genomics, has so far successfully explained the origin and dispersal of IE languages and culture in Europe, we find that several elements must be reinterpreted to account for Asia. First, we show that the earliest unambiguous example of horse herding emerged amongst hunter-gatherers, who had no significant genetic interaction with western steppe herders. Second, we demostrate that the Anatolian IE language branch, including Hittite, did not derive from a substantial steppe migration into Anatolia. And third, we conclude that Early Bronze Age steppe pastoralists did not migrate into South Asia but that genetic evidence fits better with the Indo Iranian IE languages being brought to the region by descendants of Late Bronze Age steppe pastoralists."
Don't know how they can state the underlined part so definitively.
And this from today's Science magazine, in the 'news' section
Finding the first horse tamers
Genes suggest that Central Asian hunter-gatherers, not famed Yamnaya herders, first domesticated horses
By Michael Price
Taming horses opened a new world, allowing prehistoric people to travel farther and faster than ever before, and revolutionizing military strategy. But who first domesticated horses— and the genetic and cultural impact of the early riders—has long been a puzzle.
The “steppe hypothesis” suggested that Bronze Age pastoralists known as the Yam- naya, or their close relatives, first domesti- cated the horse. Aided by its fleet transport, they migrated out from the Eurasian steppe and spread their genes, as well as precursors of today’s Indo-European languages, across much of Eurasia. But a new study of ancient genomes, published online in Science this week, suggests that the Yamnaya’s effect on Asia was limited, and that another culture domesticated the horse first. “This is a really exciting paper,” says Priya Moorjani, a genet- icist at the University of California, Berkeley.
The first signs of horse domestication— pottery containing traces of mares’ milk and horse teeth with telltale wear from a riding bit—come from Botai hunter-gatherers, who lived in modern Kazakhstan from about 3700 B.C.E. to 3100 B.C.E. Yet some research- ers thought the Botai were unlikely to have invented horse husbandry because they lin- gered as hunter-gatherers long after their neighbors had adopted farming and herding. These researchers assumed the Botai learned to handle horses from nearby cultures on the steppe, perhaps even the Yamnaya, who were already herding sheep and goats.
Genetic data suggest the Yamnaya mi- grated both east and west during the Bronze Age, and mixed with locals. Some research- ers hypothesize that they also spread early branches of a Proto-Indo-European (PIE) language, which later diversified into today’s many Indo-European languages, including English, Italian, Hindi, Russian, and Persian.
To explore the Yamnaya’s legacy in Asia, a team led by Eske Willerslev of the University of Copenhagen and the University of Cam- bridge in the United Kingdom sequenced the whole genomes of 74 ancient Eurasians, most of whom lived between 3500 B.C.E. and 1500 B.C.E. The researchers devised a rough family tree and timeline for these samples and those from later civilizations and modern people.
The team found no Yamnaya DNA in the three Botai individuals, suggesting the two groups hadn’t mixed. That implies the Botai domesticated horses on their own, says Will- erslev, first hunting the animals, then man- aging herds for food, and finally using them for other purposes. “It’s an extremely impor- tant achievement from a group of people we all think of as being pretty simple,” he says.
The new work fits with the archaeologi- cal evidence and a recent study of DNA from ancient horses themselves (Science, 6 April, p. 111), says zooarchaeologist Sandra Olsen at the University of Kansas in Lawrence, a co-author on that study. That work showed that Botai horses were not related to modern horses, hinting at separate domestications by the Botai and other steppe dwellers.
The Yamnaya used horses to migrate far and wide. Yet Willerslev’s team found little Yamnaya DNA in Central and South Asia. They saw no trace of it in ancient people from Anatolia in modern Turkey, where Hittite, an early branch of PIE, was likely spoken. That suggests Hittite likely didn’t evolve from a language brought by the Yamnaya. “What we see does not support a classical way of look- ing at the steppe hypothesis,” Willerslev says.He argues for a more nuanced history in which steppe pastoralists weren’t the original horse-whisperers or first introducers of PIE to Anatolia. But by seeping into Europe and Asia in multiple migrations, he says, they still rode their steeds to a big role in prehistory.