Khanate of the West:
Let’s try this again. I may be borrowing some things from B.Munro/Quantumbranching like the fate of the Osman family, the Swahili states and France. If anything else does come up it will likely be a coincidence. Also decided to keep the closed borders on most unclaimed land again.
In this time-line, Ogedai Khan lives a little longer and his armies are able to continue their invasion of Europe. Like they did in Persia and China, the Mongol hordes are able to rampage through Europe, cities are burnt, populations are displaced and the Pope, like the Caliph before him is tied into a sack and trampled in honour of his holy state. Europe is crippled and traumatised much like the rest of Eurasia before it. A second Scourge of God.
Expanding even further than OTL, did no favours for the Mongols and the division between the eastern and western halves of their empire was exacerbated by the thousands of often violent Christians. The Mongol Empire eventually divided and collapsed even earlier than OTL but in a very different fashion that had even wider repercussions for all of Eurasia. A few successor states do emerge in Asia but the Mongol presence proves to be far weaker than it appeared. The changes they do cause, however are enormous and far reaching.
It is now the year 1852 AD.
The Yuan Empire is the largest of the post-Mongol states. The Mongol administration and colonists were long ago assimilated by the Chinese and there is little that remains of the Mongol cultural influence. The Mongol homelands are part of their empire but feel little connection with their overlords. The Yuan eventually followed their southern cousins across the sea and set up their own colonists. Led by numbers of Mongolian horsemen, the Yuan have thrust far into the Great Plains. The Yuan have failed to properly keep up with their rivals in terms of technology. In the last war with the Spanish, their numerically superior fleet was destroyed by the more modernised European fleet. Their cousins to the south broke away from Mongol rule completely under a new dynasty, the Tai Dynasty. They have been in a perpetual state of on and off warfare with the Yuan. The Tai also proved to be far more enthusiastic with sea travel and have set up a number of profitable colonies overseas. Their greater contact with other cultures has also allowed them to modernise far more than the Yuan. The new technology may yet prove very useful as they prepare to launch a new war to reunite China at last.
In Europe, the last surviving Hapsburgs manage to pull an Osman and build a mighty empire from their headquarters in the Swiss Alps. The Hapsburg Empire is a more homogeneous nation than the previous Holy Roman Empire and has even expanded into many of the post-Mongol states. Their biggest problem is in Eastern Europe. The invasion of the Mongols, lead to numerous migrations. The area around the Baltic, Poland and Hungary are as ethnically and religiously messed up as the OTL Balkans. The Hapsburg Empire used to stretch further but has declined somewhat since their heyday. The new Papacy was set up in Innsbruck where they are subordinate to the Emperor. Rome has been rebuilt but it is still smaller than it was before and many of the monuments the city was famous for have not yet been rebuilt.
Several of the French states have been united under a harsh theocratic kingdom that houses their own Pope and opposes the Hapsburg Papacy. France is highly repressive and fanatically Christian, examples of mass flagellation and witch hunts are still common but the people have largely given up the extermination of their neighbours for the promise of crusading against infidels across the sea. The French regime is also not against technological advancement and though they have banned a few scientific theories concerning geology and archaeology, they have done their best to keep up with innovations made overseas. Spain was formed by Castile who managed to conquer many of the other states of the Iberian Peninsula. Spain cottoned onto the discovery of the Americas and did invest in them like OTL. However they had a more difficult time of it than OTL. They have lost many of their colonies but a few are left that they have gone to great lengths to convert and assimilate. After cutting most of their losses in America, they are moving into Africa instead.
The Irish felt even more pressure than OTL and eventually a small diaspora began to flee in several directions. One group eventually fled west across the sea and discovered the Americas (here known as the Braseuls). Unfortunately the states of the Irish Diaspora failed to properly survive against the natives. The few surviving states are a mixture of Irish-Amerindian culture and have now all been conquered by the British, just like their relatives across the Atlantic. The Empire of Britain was formed from the Kingdom of England which eventually managed to unite the British Isles. Britain received numerous refugees from Western Europe who fled the Mongols during the invasion. British identity and culture is a bit different compared to OTL. Like France and Spain they also refuse the legitimacy of the Hapsburg Pope and follow a form of nationalist Catholicism. England is currently turning into an enthusiastic coloniser. Their colonies are usually characterised by a dispersed agricultural style or a more compact royal company design. However their settler colonies are now becoming very populous and the local aristocrats and landowners are beginning to flex their political muscles.
Due to the different approach to colonisation and the slower progress made, a greater number of Amerindian civilizations survived. Diseases did ravage the populace but some of the more advanced and homogeneous native powers weathered through. They eventually picked up metallurgy, writing and draft animals from the colonists. Gunpowder came quite a bit later but by the time the colonial powers arrived in force the natives were more capable of putting up a proper fight.
The Aztecs did come to power but the arrival of Europeans in the region displaced things. The Mixtecs were some of the first peoples in the region to obtain European technology. Using new metal weapons, they defeated their Aztec masters and carved an empire of their own from Mesoamerica. The Mixtecs have since converted to Christianity and adopted a number of European customs and practices into their empire. They are also a flamboyant culture with numerous colourful and macabre festivals and celebrations that often compliment the imported Christian festivals. They still speak their native languages, with an alphabet adapted from the Mayan script. However their language has incorporated a number of loan words from Spanish and English. The Mixtec Empire has experienced a new wave of modernisation under their recent Emperor who is an enthusiastic progressive and technophile. He has worked hard to install as many new technicians and engineers into his government as possible and passed a number of decrees that should advance his nation.
Many other Amerindian states were eventually conquered by European powers but several have shaken off their colonial yokes. The Kingdom of Khimu is a former Spanish colony and was named after the largest native power in the region during its colonisation. A local governor led the creole colonists in a rebellion against the Spanish and successfully ousted them. He proclaimed himself king and has descendants still sit on the throne. The nation is now majority creole and has since begun to actively discriminate against the remaining natives. The Maya are now Spanish speakers and Christian but did a better job of preserving their indigenous culture and staving off the Mixtecs. The Great Plains still have a few independent kingdoms and confederations but they are slowly being conquered by the more advanced and organized colonial powers.
The collapsed Mongol Empire left Eastern Europe in shambles. For a time the Golden Horde lingered on for a while but eventually even they crumbled. The various principalities of the Rus suffered more than OTL. Muscovy was obliterated during an attempted rebellion and its inhabitants were slaughtered. Instead as the Horde receded, the state of Novgorod rose to prominence. The influx of refugees from the other Rus states and further afield provided them with the manpower to expand. Russia unfortunately found itself confined by the stronger Mongol successor states, the vibrant Osmanli Empire and the Hapsburgs and so stagnated for awhile. As of the 18th Century, they have been revitalised under a series of talented Tsars and have even expanded into Eastern Europe as the Hapsburgs declined.
Butterflies forced the House of Osman in a slightly different direction and after almost dying out, they managed to make it into Persia. From there they have built up a decent sized empire in northern India. At one point, their empire stretched from Syria to the Ganges but they since contracted to their core territories around Persia and Mesopotamia. The Turkic elements of the family have now been completely assimilated by the ruling Iranians but the name is still applied. The Turks of Anatolia have waxed and waned several times since the Mongols pulled out but failed to rise to full prominence. In the meantime, the Mamelukes have built a decent sized empire based at Alexandria that has worked hard to keep up with their rivals in the region. However as Europeans continue to spread their influence further, their grip on power may really begin to weaken. Much like OTL, the nations of India are being colonised and puppetised by other colonial powers. However nearly all of the players are different to OTL and how the Great Game will be played out over here, has yet to be seen.
Technology is the same as OTL levels of development. However it is far more widespread in areas whilst more backward in others. Industrialisation is beginning to catch on and the scientific method has been developed and spread to much of the world. Asia and OTL Latin America have done a better job of keeping up with technology whilst much of Europe has actually fallen behind. Religion is also different, especially in Europe. The Protestant movement never took off, though numerous schisms have split the Catholic Church and divided it up between the various nationalised churches. Slavery has been abolished in the western world and is beginning to naturally phase out in many other prominent nations across the world. Democracy is also not a widespread concept. There have been no republican movements yet and even the idea of a constitutional monarchy (of the OTL type) would be considered incredibly radical. Colonialism is still profitable and the powers that be are scrambling to get as much as they possibly can. As tensions rise over influence in Asia and technology makes entering the tropical regions easier, there may yet be Scramble for the Planet.