Let's analyse the map first.
IOTL, there was the Manchu Khanate, then Hongtaiji changed its name to " Great Qing State" as the Khanate was becoming more and more of a player with affairs within China. Then, as Qing was exposed to western concepts of "empire, kingdom, or republic", they changed their formal name to "Great Qing Imperial State", or Qing Empire. In no circumstance would the Qing downgrade themselves to a mere
Kingdom, unless they were reduced to some sort of client state of Someone else's.
Chu. The Chu in Warring States Period was today's Hunan and Hubei. The dynastic name suggests that China was being ruled by someone(and his clique) from the two provinces, which was very likely with a 19th century PoD as the Hunanese soldiers was the main force in putting off the Taipings.
Tibetan Autonomous Region. The name "Autonomous Region" strongly hints communist influences as the commies love word-redundancy. Perhaps there was a leftist revolt in Tibet against the China-backed Lamas, and Chu, under a Leftist government, compromised by granting Tibet autonomy.
Colors. Greater Mongolia and Xingjiang were colored similar to Russia, hinting Russian influences or even colonialism. Based on the similar colors of Chu and Qing, we assume that Chu subdued Qing.
Xingjiang. It's a Chinese name, hinting a Chinese-dominated (Han or Hui) Xingjiang taking orders from Russia?
TL:
Due to strategic misjudgements, the Qing failed to contain the Taiping's northern expeditions, and fled West to Shaanxi. When the Muslims started to rebel(otl), a good part of the Qing Royal house was wiped out.
Xiang (Hunan) Clique, a royalist force, now have nobody to be loyal to. Not willing to kowtow to the heretic (unconfucian)Taiping, the Hunanese soldiers declared Zeng Guofan their emperor, despite Zeng's own loyalty to the Qing house. The Qing government (on the run in Manchuria) killed many of Zeng's family when they heard Zeng's "treason", forcing Zeng to really accept the title Emperor of Chu.
At the same time, Taiping Heavenly Kingdom was suffering from its own victories. Wei Changhui launched a coup against Yang Xiuqing, killing his entire family. Shi Dakai, disappointed by the infighting, fled to join the Taiping force in the north, who happened to be Yang Xiuqing's loyalists. Shi Dakai declared that with Yang Xiuqing dead, he was the new Reincarnation of God, and he was to save Hong Xiuquan from Wei Changhui. Thus we now have two Heavenly Kingdoms based in Nanjing and Beijing, respectively.
Now China is in complete chaos. Shaanxi and Gansu in the hands of the Muslims, Central Plain the Northern Taipings, Jiangnan and Jiangxi the Southern Taipings, Xingjiang the Yakub Beg, Manchuria the Qing, and the rest of China was maintaining a weak stability under their own provincial governors.
Gradually, upon realising that reviving Qing was impossible, the provincial governors shifted their allegiance to Chu. In a war no less bloody than OTL, the more united Chu was able to beat the Taipings.
Meanwhile, Russia invaded China, and was able to gain much more than they did IOTL due the collapse of the Qing. Outer Manchuria was completely annexed (as per Aigun Treaty IOTL), Mongolia and the rump Qing was puppetized, and Yakub Beg was toppled with the help of Chinese Muslims(Hui), that's why the new Russian protectorate was called Xingjiang, other than Kashagaria.
Zeng Guofan wiped out the Taipings and united China, only to find out that a large chunk of it was gone. However, China was in no position to fight another war. Zeng signed a treaty with Russia*, inaugurated a series of reforms, waiting for the chance to take revenge on the Russian backstabbing...
*In China, it's a rule for a new dynasty to treat the descendents of the previous dynasties' emperors with dignity, as a measure to boost the new dynasty's legitimacy as the legal successor of the old one. Zeng Guofan therefore gave the Yuan, Ming and Qing descendents princely title in respect to this custome, and as a protest against Russian dominance over Manchuria and Mongolia.