This is an interesting question, with a difficult answer:
First of all, I don't think our friend Dimm has the answer. His vision of European expansion is, at least, dreadfull. The Portuguese, for instance, were not intended to "kill, rape and enslave" everyone in greater extend than, for instance, Almoravids in Iberian Peninsula, or the Ottomans, or the Japonese in Korea, or the Dutch, the French, the English. As for the Spanish, unfortunatelly, that seems to be another matter...
I think that the main causes for Europe's power were poverty, curiosity, open mindness and the resolve to go abroad.
1 - Europe was in fact very poor, specially if compared with the Chinese or the Muslims. There's allmost no gold nor silver in Europe, and our products were not competitive in the World market (rough quality and not extravagant enough). The only way to get economic power was to crate better vessels, better technologies, better weapons (cannons and muskets!) and to venture in exploration and conquest.
2 - Wille the Chinese and muslims, namely the Ottomans, closed themselves because they considered to be the best (the muslims acctually considered that, after having "islamicized" Aristotles and the Greeks authors, they had reached the apex of knowledge and civilization!), the europeans kept grabing whatever they could in terms of other peoples' knowledge and science. That allow them to surpass everybody else. The Portuguese, for instance, used the Templars (the Order of Christ), jewish and moorish knowledge, algebra, mapmaking and medicine in their explorations, and also the christian faith, to bolster their resolve to conquer and keep their new found lands.
3 - Another reason for european power was the discover of the Americas, which allowed the Portuguese, the Spanish, The Dutc, French and, mostly, the British, to explore extremely rich lands and to send emmigrants, thus avoiding overpopulation. The great amount of wealth enable them to create a better economy and army/navy.
4 - One more, and important, reason was the political change, in which feudal states gave place to modern ones, in which there's only a political power (the Portuguese, for instance, did that in 1385. Maybe that's why they were the first to go overseas and conquer Africa, the Americas and Asia...?). While the Ottomans were becoming less and less centralised, the europeans were becoming more "modern".
So, I think these are some the reasons. Each one, for it self, is not good enough. Togheter, they allowed great deeds. That conjunction happened only in Europe. And thus, History was made
Best
Sikander