For the relatively small percentage of koreans who go into sports or dance etc. they go all in. It's not really about balancing school and sport, it becomes all sport. Why do you think that korean skate stud moved to Russia? Korean pride is huge and to leave Korea for Russia was a move of desparation because his whole life was based on skating and for some reason he was getting blackballed by the korean skate federation despite his talent. Most people can't imagine what a heavy choice it must have been to leave Korea, with it's tradition and passion for short track to go compete for another country. Apparently he almost went to the US but got more money from Russia.
As for the others, most go to a sports university that is located at the olympic park in seoul, where there are ice rinks and reminders of the Olympics all around them every day.
Comes down to:
1) large population of natural body builds for the event
2) large population of extremely determined and focussed people to pull from
3) total commitment to the sport once they have shown promise
4) excellent training partners/rivals = 1000's of hours of highly competitive practice
5) a chance for national fame if you rise to the top, which is more akin to being the olympic champ at 100 meters in track if you are in a lot of other countries like the US