No one rules it. It's independent and certainly not just 'trying to be.' Aside from what is today Turkmenistan and Uzbekistan, which are under the sway of the Ottomans, and the eastern limits past Lake Balkhash which may or may not be a part of China everywhere there is under the control of native polities AFAIK. This is looooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooong before anyone could actually tame the steppe.Who controls the central Asia? Is it divided between Russia and Ottomans and are there any independent (or at least trying to be) states there? Maybe even China could try to step into this region? As I can see this region could play more important role then it does in OTL.
IOTL Russia only started pushing south rather than east in the beginning of the 19th century and they didn't get very far until the mid-19th due to the collapse of the Khazakh Khanate into three competing tribal polities. This initiated a slew of military activity in the 1860s and 70s where they conquered or vassalized the native Khanates of Khiva, and Kokand as well as the Emirate of Bukhara. This was assisted by Kokand having been in civil war for the past 20 years, and gave the Russians one hell of an initiative to disrupt the balance of power in Central Asia. The only reason they were properly able to accomplish this quick conquest was because of a revolt of the Muslims in Dzungaria that occurred at the exact same time and which saw Chinese authority collapse in Xinjiang and their influence vanish from Central Asia. The power vacuum gave Russians an opportunity to act with impunity and even the British weren't in much position to stop them, as Afghanistan had prevented British expansion earlier in the century and both the Sikh wars and the Sepoy Rebellion tied their Indian forces down during the century which kept them blocked from Central Asia. It took the Second Anglo-Afghan War in 1878 for British to have actual physical presence in Central Asia but by then the Russians were at the border of Afghanistan. The only other player, Persia, had lost a slew of wars to Russia over the past two centuries over the Caucasus and had long since been cowed. They were in no mood to get involved in yet another war with Russia after the last ones in the early 19th century. Russian conquest didn't really 'end' until 1895 when the Pamir Boundary was formed between British Afghanistan and Russian Central Asia but there was still intermittent warfare and small raids among tribal leaders that continued to plague the region until WWI, which wasn't much better but that's past the scope.
The conquest of Central Asia was a shockingly brief period after a century of preparation and posturing that was only really possible thanks to the advent of industrial technology, the rise of modern empire, and an incredibly favourable geopolitical situation. Central Asia won't be seeing much impact in the story until that point other than for polities who neighbour it, almost exclusively Persia. China isn't going to be doing much there, they have never had reason to expand into it and are entering an isolationist phase following the war with Korea. Their goals are to keep their borders and take back China, they are not out for imperial expansionism. It is highly unlikely that Central Asia will play a greater role than OTL. It may end up with a more complex history of independence as a battleground if B444 wants it to but it's still one of the most isolated regions of the inhabited world without much of value other than to facilitate transportation between wealthier resource-producing regions. At least until natural gas becomes important. And that's of particular note here, because immediately after the Russian Conquest they built the Trans-Caspian Railway and planned the Trans-Aral (which started construction in 1900). Both of these were to facilitate Russian access to the east, and were necessary to the maintenance of power in Central Asia in the same way it was to the vast plains of the American West. And on the subject of America, the American Civil War caused global cotton prices to skyrocket. Russians (and later Soviets to a much higher degree) intensive cotton cultivation along the Amu Darya and Syr Darya. Historic production had been relatively low but with higher cotton prices that low production became much more valuable at the same time as the Russian conquest. The Russian government did not enjoy the prospect of another spike in Cotton prices, especially since the order of the day was Mercantilism, so while they were building the railroads to expand transportation for soldiers and access to trade in China, India, and Persia they were also reorienting agriculture in the region towards Cotton production. Extensive cultivation of cash crops in central asia forcibly tied them to Ukrainian and Russian food production, as well as the newly constructed railways. This tied the economic livelihood of the average central asian (other than Khazakhs since their land can't be irrigated so they instead had wheat forced on them) intrinsically to the well-being of the Russian state.
You shouldn't assume it's a place that's bound to be conquered, let alone one that will be conquered anytime soon. Central Asia resisted foreign invasion for centuries due to its isolation from seapower, vast and resource-poor steppeland which made secure rule difficult, militarized and mobile society which made conquest and maintenance challenging until the entire economic and social order could be changed to facilitate foreign rule, and by playing their imperial neighbours who wanted trade off one another.
That was a lot longer than I originally intended it to be but central asia's a damn complex place.