What determines which culture will be the most dominant one is not one single factor, and some of them look completely random. For example, China invented movable type printing before Europe but Europe had an alphabet of discrete symbols that were optimized for stone engravings while China's alphabet was optimized for writing by hand quickly and with room for expression. That was one of the factors of why Europe could start the printing press revolution to democratize science and information.
I'm lucky to be living in Sweden in 2017, I would however want to move if this would've been 6th century Sweden.
Of course al-Khwarizmi wasn't the first or only person to "discover" algebra - he was building off of 2000 years of Greek, Persian, Arab, and Indian work.
The point wasn't that he's another great man[1], but that it's simply incorrect to talk about "Western science and technology" as if they're either isolated or monolithic -- they're neither.
If al-Khwarizmi hadn't have been Latinized and become the reference for Western mathematics until the Renaissance, then someone else would have. But that someone else would have come from the "Eastern" world, simply by virtue of where the relevant research and academic tradition was at the time.