I know nothing about China but the impact on the Middle East is mind boggling ...
I know.
Would point out that you'd probably get a dynamic of pottery using foragers from the PC steppe contacting other neolithic cultures and ultimately adopting ox-drawn wagons and some kind of pastoralist expansion into the steppe, even with no horses and the Yamnaya / Afanasievo cultures specifically as we know them butterflied away (some kind of domesticated ruminants and grasslands is enough). It's not out there that cultures could have travelled as far as the Afanasievo did from the PC steppe, without the horse.
Contact between ceramic age steppe foragers and neolithic agriculturalists occurred from the 6th millennium BCE onwards, so before my PoD. And yes, herding of ruminants is adapted by the former in my TL (it already was around 5200 BCE by Dnieper-Donets).
But ox-drawn wagons are still very far away because IOTL the wheel was invented in Mesopotamia. IOTL, the idea disseminated into the PC steppe in the second half of the 4th millennium BCE through the intermediary Maykop culture of the Caucasus. But that happened in an environment in which steppe pastoralists WITH horses were already moving about quite a lot, both in the steppe and into the Danubian lands (beginning towards the end of the 5th millennium) as well as Eastwards towards Afanasievo (from the middle of the 4th millennium BCE onwards). With David Anthony, I believe that PC steppe pastoralists began riding very early, in the second half of the 5th millennium BCE already. Without horse-riding, I can't see that kind of mobility emerging prior to wheeled vehicles.
Now, without the massive increase in mobility evidenced in the PC steppe and its fringes in the 5th and 4th millennium BCE, when is the wheel likely to reach them? The Caucasus is a formidable geographical barrier against the dissemination of innovations and, without either horse or wheeled vehicles, also against the movement of people. I suppose in the horse-less world of my TL, the innovation of the wheel is first going to spread into the Levante, and from there into Egypt and across Anatolia and into the Eastern Mediterranean, and from there into the Danubian sphere. By the time it gets there, it's already in the Northern Caucasus, too, so roughly around 3000 BCE, which would be three or four centuries after OTL, it could reach the steppe cultures from the South, both in the frontier / contact zone along the Dniester and in the frontier / contact zone of the North-Eastern Black Sea coast.
With ox-drawn wagons, they COULD undertake an Afanasievo-like migration (albeit more than half a millennium later, which in itself should have severe butterfly effects on China, too). But I still think it more likely that they don't. The Yamnaya / Afanasievo expansion happened because a steppe cultural horizon had emerged which was highly prestigious and which caused other groups to adapt to it or enter symbiotic relations with it. Without the raids horse-riding allowed, without the emergence of a warrior class, without the emergence of what Anthony calls the Proto-Indo-European "guest-host" concept, occasional migrations caused by strong push or pull factors may occur, but they won't necessarily cause the receiving regions to alter their cultures massively due to the influence of the newcomers. Also, with wagons but without all the above-mentioned changes related to horses, the occasional migration need not initiate a long-lasting transmission belt of cultural innovations which OTL's steppe highway was. Instead, a group of migrants may well have "gone native", keep the wheeled vehicles and pass them on to their neighbors, but otherwise adopt, maybe linguistically, religiously, and with regards to what animals to herd, how to hunt other animals, and which plants to possibly cultivate.
Long story short:
I stick with the equation of No horses = no significant contact across the Eurasian steppe affecting the cultures in what we call China and its neighborhood.
Arguably there is a recession across the late Bronze Age and into the Iron Age to classical period of many semi-sedentary steppe cultures like the Sintashta / Andronovo complex, in favour of more nomadism, due to the way horses began to be used. (Some of the most prominent sites of the Sintashta culture were not called "The Country of Towns" for no reason -
https://en.wikipedia.org/wiki/Country_of_Towns). Possibly we would have ended up with a more sedentary culture thriving on the Russian steppe earlier in history, and likely more of an early civilization of what would be best described as Russian / Northern European-like people (from what we know of these semi-sedentary / sedentary post Yamnaya early cultures like Sintashta, though the cultural butterflies would be huge). Though this all depends on our perspective on how important the horse was to early steppe cultures.
As argued above, I would think that none of these cultures would emerge at all. East of the Easternmost Volga bend (Repin culture), in whose river valley any horse-less post-Samara steppe culture will remain centered, with or without ox-drawn wagons (cattle were increasingly difficult to feed in harsh steppe winters after successive climate changes leading to colder and more arid steppe climates...), I don't see much reason why we wouldn't just have ceramic forager cultures like the
Kelteminar in the South or the
Pit-Comb Ware in the North, for a long, long time. Like, well into the 2nd millennium BCE.
Now, back to my initial question:
What does that do to China, to the Yellow River cultures primarily, but also, when these started to dominate other parts of china IOTL, to the coastal, Yangze and North-Eastern cultural complexes? Is the focus shifted or not? Do they overall fare better (because no aggressive steppe nomads from the late 3rd millennium BCE onwards) or worse (because no transmission of bronze metallurgy, horse-riding, wheeled transportation etc.)? Or do they simply develop differently (but not necessarily faster or slower), like e.g. less centralised but also with less disruptive shocks? Or...?