You have a very weird definition of luck. Most of what you list I call biology and geopraphy.
And I bet anything related to human behaviors is psychology and sociology. Luck doesn't mean something is causeless.
Christianity unyting Europe? Maybe try reading some basic history book of the time period of Europe. Spoiler: Religious wars will be pretty prominent, bloody and at times incredibly destructive - and highly divisive. A great boon and huge luck indeed. I also have a hard time imagining what you mean by a united Europe: thats a great idea that never in history came to existence - at least this far.
Not uniting them as one country. I mean giving them a shared institution (Catholic Church), and a reason to see each other as something more than rivals to be mercilessly conquered. Not to mention the fact that it granted kings legitimacy with the divine right to rule idea.
And how did the europeans not play by the same rules? They die just as easily as any other people, they are neither inherently smarter or tougher than others. The rules were the same. That in this time period they used their initially very meagre resources in a way that enabled them to conquer more resources and finally conquer a big chunk of the world means that they were doing something seriously better than the others - if the goal was conquest and looting that is.
For many parts of the world, large-scale conquest and looting wasn't on the agenda, but that doesn't matter.
The bigger part has already been outlined. The Ottomans put them into checkmate by destroying Byzantium and disrupting trade along the Silk Road, and then they discover a previously unknown route to India that can compete with the Silk Road (by going around Africa), and simultaneously discover two massive, mineral-rich continents whose populations are easily swayed into allying with your explorers and who have a tendency to die to disease when contact is made, making conquests and establishment of legitimacy a breeze. If any writer pulled that in a novel, it would be decried as pure bologna. 7.8/10? More like 3/10. The writer needs to stop and re-evaluate his life, because this clearly isn't the right profession for him. Imagine if this happened in World of Warcraft. The Alliance manages to cut off Horde trade and corner them. Their tech was enough to destroy Orgrimmar, and they have every reason to win.
Suddenly, the Horde discovers two more continents that are filled with pushovers, gold, silver, and exotic goods, while simultaneously finding a way around the trade lockdown. They steal whatever tech they can, and use this newfound Deus Ex Machina to eventually destroy the Alliance. That's not a twist. That's bad writing from a Horde fanboy.
I'll repeat it here so the point isn't lost.
Christianity existing to unite Europe? Luck.
Columbus screwing up Italian and Arabic miles but still reaching the New World? Luck.
The Aztecs having the gold Europe needed when the Ottomans were about to cause a continental economic crash? Luck.
The natives who owned those resources being extremely vulnerable to Old World diseases? Luck.
The Aztec capital encountering a famine right as the Spanish-led coalition is on its doorstep? Luck.
All of this happening as the Inca, people who based their Empire's legitimacy on its ability to expand their borders and who built a massive road along the Empire, running out of land to conquer? Luck.
South America being covered in mineral riches? Luck.
The North Sea being just inhospitable enough for the British to be able to get away with privateering Spanish gold? Luck.
An ocean route to India existing? Luck.
The Muslims who occupied Iberia just happening to have the technology required to sail for long distances, but not using it for Atlantic exploration earlier? Luck.
Africans being able to survive the working conditions for farming sugar? Luck.
Kilwans lacking the ability to fight off Portuguese exploration vessels? Luck.
The Indian Ocean being chock full of goods that would sell well in Europe, right as the Europeans came into possession of extremely high amounts of mineral wealth through the Americas? Luck.
Literally everything that happened in India? Luck.
They were given a technological catch-up button with the Silk Road and the fall of the Byzantine Empire, a crap ton of mineral wealth from the Americas, sailing technology from the Muslims, and the perfect position for snowballing, since they got their wealth by looting the existing trade routes from half the globe away. All the while, Eastern Europeans were loyal enough to their faith, something they got from Israel, to defend them instead of turning on them to loot them for the gold they were bringing in.
If Europe was playing according to the same rules as everyone else, they would've collapsed from the Ottoman disruption of the Silk Road's trade. They would not have found two continents full of Deus Ex Machina set specifically to be easily conquered right as the Europeans arrived.