He would go on to conquer Europe, taking the opportunity presented by the discontentment over the legitimacy of the Holy Roman Emperor. It would be his toughest campaign, true, but Zheng He was a brilliant admiral. The combined Chinese and British naval expertise would prove detrimental to continental resistance. However, it would not be cakewalk as discontentment over Chitish (Chinese-British) heavy-handedness spawns revolutions all over Europe. A Reign of Terror and conflict between European countries would pave the way for the rise of Napoleon. However, Napoleon would succumb to a Spanish Ulcer masterminded by the Chitish with their Basque allies (having promised the latter a free homeland) and the Russians would come and try to grab a slice of the pie from the East. Unfortunately, China opens an Eastern Front with Russia. The Tsar falls and the Bolsheviks take over, after which Russia enters a period of bloody civil war.
At this point the Chitish, under Zheng He's deity-like guidance, would have conquered all of Europe except Russia. What happens next is difficult to say as it depends on whether Stalin comes to power and industrialises Russia. And maybe the Nazis will eventually take over the Chitish political system and launch a disastrous campaign in North Africa, which will be defeated by the forces of the Free British under Montgomery (who might be funded by Cecil Rhodes). If that happens then the Nazis will lose the front against Russia and will be conquered by the Allies (under the Confederate States of America) and the Soviets.
Of course, all this is moot if Alexander had lived to conquer China. Surely everyone would have heard of his god-like powers and flock to him in his campaign against the Warring States. Even the Warring States themselves would willingly submit to him in order to defeat the archdevil Qin Shi Huang, who is hated by the Chinese even more than some invading Western 'barbarian'.
PS: And, oh, Genghis Khan would never have come to power as the Chinese are able to stop him. However, his descendant, Roman Ungern von Sternberg will plague Siberia with his horde of marauding but disorganised soldiers, only to be defeated by Chiang Kai Shek and Mao Zedong under the United Front.