Here is Uncle Holden's grand TLDR of why each region fared the way it did.

To win the game of civilisation, a nation state requires....

A Safe Home Base - A landmass possessing friendly geography with natural barriers to invasion and enough consistently fertile ground and clear/easily cleared spaces that allows a nation to take root and expand without being catastrophically disrupted either by natural phenomena or by dangerous neighbouring nations. Having this will allow the for a good standard of....

Innovation - The inception, refinement, adaptation, perfection, and experimentation with new concepts, technologies, techniques and tactics that allow a civilisation to have a huge advantage in both satisfying its people and staying above its rivals in every field, which is hugely reliant upon...

Competition - External motivators that pose enough of a threat to a nation's sovereignty/prosperity/pride/safety/influence for both a nations government and private citizens to invest large amounts of time and energy and expense into finding and developing any advantage they can. However to implement any such advantage will require access to a good number of...

Resources - A nation requires access to a resource that is in existential demand within its borders and in other nation states both nearby and worldwide. To control the entirety/a high percentage of this resource will give a nation far more sway than a nation without such resources, and will make other nations more willing to ally or at the very least make war, and most importantly this gives a nation a vital stake in global...

Trade - Trade of both of commerce and ideas both enriches a nation and enhances its access to the above factors, since it makes the spread of innovation far easier, enhances national and international competition in a non destructive manner, and allows access to resources that the nation does not posses within its borders. Furthermore being strongly linked in to the global trade network means that your national immune system to diseases from all over the world gets continually stronger since they will always be brought within your borders by carriers both human and animal. However international trade's most basic requirement is that a nation has access to...

The Sea - In order to move huge amounts of people/resources in the pre-modern era you need ships. To have ships you need access to the sea. The more access to the sea a nation has (i.e. having it form most of your border like Spain or England) the more opportunity it has to improve and perfect its ship technology and sailing techniques and the more willing the nation's elite will be to fund trade ships and a powerful navy to protect both trade and national sovereignty.

Europe
Perfectly Friendly geography (effectively every subregion was a short distance away from the sea, allowing ports for trade, navies, and the exchange of ideas) and countless natural borders allowed dozens of nation states to develop into urbanised societies, while also ensuring they were in fierce but non catastrophic competition with eachother in every military, scientific, economic, and cultural field which drove innovation into overdrive across the continent since each new development could be easily shared due to common languages. Also the closest continent to the americas which served as the ultimate "I WIN!" button.

East Asia
Geography was too damn friendly, allowed vast (and more importantly, long lasting) hegemonies to be built which slowed innovation (and subsequent copying and upgrading by rival nations) to a snails pace due to a lack of real competition. Also due to the specific cultural factors (i.e china's specific "FACK YOU BARBARIANS WE CENTRE OF THE UNIVERSE!" foreign policy and national mindset) they were far less interested in adapting and experimenting with innovations from other continents even as their own innovations (printing press and guns) were perfected to levels beyond imagining by Europe. Thus they end up being bitchslapped by Europe for a good few centuries until their level of development and industrialisation matches it.

India/IndoChina
Geography decidedly unfriendly with city states existing as virtual islands in dense jungle, which led to conflict and competition that was both fierce and corrosive to any significant mass innovation. While coastal cities were hubs for trade, trade ended up being controled by europe and its far more developed navies/economies.

Middle East/North Africa
Very friendly geography....initially. resources and fertile farm land were fairly plentiful, but the natural barriers prevented any long lasting innovation stifling hegemony being formed, and like europe there was access to the sea for most nation states, and like europe there was a drive to both innovate and adapt/improve upon foreign innovations which combined with the middle east being effectively the global crossroads is why for a good chunk of medieval history the Islamic empires had a solid edge against europe. However being the crossroads meant that they suffered incursions from all sides, with both europe chipping away at their power in the west, and the mongols ripping their shit apart from the east, which by the late 1400s left them decidedly weaker than europe, but the Turks' decision to strangle trade routes to europe from the far east truly sealed their fate of being utterly sidelined in the global arena since it gave europe the motivation to seek alternate routes which led to the discovery and colonisation of the americas.

Sub Saharan Africa
Utterly shit geography. Rain was almost never regular enough to form permanent urbanised societies across of the region, and between the out and out deserts, disease infested jungles, and inhospitable Savannah, there was never any ability to advance beyond vast numbers small scale tribal groups across the continent. This meant that innovation beyond "perfect surviving nomadic farming/hunter gathering lifestyles while fending off rival tribes" was effectively non existent with a few exceptions. While there were rich resources on the continent, extracting, utilising, and trading them on any nation-building scale was out the question with that level of development. In the few areas that lucked out on hospitable/fertile geography however nations as prosperous and innovative as any in europe or the middle east sprang up, and they became a key link in the global chain of trade, though their lack of serious competition from their nomadic neighbours and their relative isolation from europe/asia/the middle east meant they could only really go so far.

Americas
All the geographic advantages and easy to access/exploit resources of Afro-Eurasia but with one fatal weakness. They were UTTERLY cut off from the global exchange system. Thus they never gained any access to the innovations of Afro-Eurasia, nor some of the most basic staples of Afro-Eurasian life such as easily domesticated farm animals like chickens and pigs and cows that could provide meat, eggs, hides, or brute farm labour, transport/military animals like horses and donkeys, nor most vitally the circulating infectious diseases that Afro-Eurasia had over ten thousand years to develop high levels of immunity to. This latter one guaranteed that they would automatically lose the game when they were exposed to whomever got to non isolated parts of the Americas from Europe/Asia/Africa first. And once they were all wiped out by the dozen different plagues that hit them their land and resources would be easily taken over. Since the Turks made europe venture out into the wide blue western yonder in order to get spice routes from india, Europe got there first. And europe reaped the ultimate reward as between the big players of Britain, France, the Netherlands, Spain and Portugal who pretty much just annexed both north and south america, the continent of europe effectively grew 10x bigger and 100x richer over the course of three hundred years.

So yeah. That's why Europe won and sub Saharan Africa remained mostly a shit hole.

These rules would also come into effect in the competition between the big European powers for a good 500 years, with Spain initially being the massive winner since it got all the south american gold, only for Britain to end up the ultimate victor due to gaining the more boring yet more in demand resources of North America and eventually the Caribbean, which enabled it to perfect its Navy/Economy fast enough to establish colonies across the planet by the time the 1800s wave of revolutions came which saw the US secede and almost all of Spain's colonial possessions being lost, leaving them with a couple islands while Britain retained Canada, South Africa, Australia, and the biggest European foothold in India.