Actually, that Europe conquered the world makes a kind of twisted sense. Yeah, they were at constant war with eachother, but war doesn't lead to technological stagnation, it does the exact opposite. Because of the constant fighting, each state had to do everything in its power to stay one step ahead of its rivals and that means more soldiers, better armour, and better weapons. Warfare breeds better weapons like an open wound breeds bacteria.
Lots of money doesn't necessarily breed lots of good weapons or lots of good soldiers. It might lead to scientific gains, but scientific gains don't always directly translate to an increase in military power. If I remember my pre-modern world history correctly, the Asian countries were, mostly, far too insular and xenophobic to bother conquering other areas, instead focusing their efforts largely on the home front, as well as importing and exporting goods. While everyone else was busy building stable, wealthy empires, Europe was building armies of well-trained, battle-hardened soldiers with the full brunt of several generations' worth of war tech development at their disposal. When you look for conquerors, you look for warriors.
