@Russian Ironically the Chinese themselves would be the greatest ally to the West in such a scenario. Yes, the Mongol Armies are powerful and pack a punch, but they were fighting against likewise lethal opponents, especially in the Song. It took a long time for them to take China IOTL, and even sped up it will be well after Temujin's death when China is fully conquered (or possibly even
if, with butterflies). Then the Mongols will have to worry about Chinese problems; assuming they conquer or try to conquer other East Asian Nations like Japan, Korea, and parts of Indochina, they now have a good third of the world under their control already. It's hard to go on a conquering spree when you're trying to hold so much down. And by the 1260s+ when they'd be done with China, many of the original Mongols will have settled down into a sedentary lifestyle, diminishing (though not destroying) their combat abilities.
I therefore find it unlikely the Mongol-Chinese Empire would go on a massive adventure to conquer the whole world like the OTL Mongols, mostly because they have so much to administrate already. Conquer and control more parts of the Steppe? Sure. Raid and exact tribute from surrounding states? Absolutely? Penetrate deep into Europe or even the Middle East? Doubtful.
It will also be interesting to see the effects on Persia and the Islamic World. The former would be a lot more populated today, prosperous and capable of being home to Large Empires like in the past.