TL;DR

"With all the pieces on the board, the key to Romania’s Olympiad success is three-fold: put the best students in the same classrooms, put the best teachers with the best students, and then incentivize schools, teachers, and students each to win Olympiads."

The easiest way to understand why it works is to imagine the opposite strategy: put the best students in the same classrooms as the worst one so the entire class advances very slowly, make the school system centered on success at sport.

(I skipped the opposite to "put the best teachers with the best students" part, because if those best students are each in a different class, one of them will randomly get the best teacher and the others won't.)