The benchmarks you cited measure scholastic ability. It is measured by such metrics as test results and graduation rates, as the second link says. The benchmarks have little implication for the general quality of life for students, graduates, and educators. Especially since getting into a top college doesn't guarantee success anymore.
Meanwhile, South Korea has the hightest suicide rate among OECD countries [1], and suicide is also the leading cause of death among people aged 15-29 [2]. Teenagers killing themselves to escape from academic pressure are so common they don't even make the news anymore. South Korean students might have the highest grades, but neither students nor educators seem to be even remotely happy about what they've got at the moment.
We're talking about a country where competition for standardized tests is so great that people pay thousands of dollars for leaked SAT tests [3]. I'm talking about the American SAT, not the Korean equivalent. Competition for the Korean SAT (suneung) gets even more serious.
In the past, when some foreign leader cited Korea's academic achievements in a public speech, Koreans felt immensely proud. Nowadays, Obama mentions Korea all the time when he talks about education policy and we're like "Err, whatever."
[1] https://en.wikipedia.org/wiki/Suicide_in_South_Korea
[2] http://www.voicesofyouth.org/en/posts/rising-suicide-rates-i...
[3] http://blogs.wsj.com/korearealtime/2013/05/28/group-of-south...