Actually this isn’t unique to South Korea at all though not to the same degree as it is in Asia to my knowledge. While not all big businesses (including conglomerate businesses) are overlooked by families especially in Asia, a good number of contemporary business conglomerates (especially the better known ones) are overlooked by families.
Family businesses aren’t entirely nonexistent in Africa, especially in Uganda as far as I know about it. (They‘re also found in Kenya, Nigeria and Ghana too.) But family businesses are a big deal in Asia. The best known examples being Tata, Samsung and Toyota. What should be remarkable is how globally famous and persistent these companies are, especially Toyota and Samsung.
In Korea and to some extent, Japan family businesses grew prominent in response to unfortunate socioeconomic situations. Perhaps as a survival method for some to make ends meet. That worked well. That and close ties with government even if it’s detrimental to some.