No comparison between the excellent economic growth of South Korea and that of Greece, Hungary, Austria, or Italy going back to either cold war or post cold war days, despite this hypothesis of "empire gradient". If you google "World Bank GDP growth <countryname>" you can find charts back to 1961.
South Korea exports consumer goods to the large US market, this has been a massive fuel for their growth. They followed in Japan's footsteps (and China, for a time at least, followed in theirs). I can't think of a single manufactured product out of Greece, Hungary, Austria and few from Italy to the US.
Being on an "empire gradient" is just an arbitrary way to look at a country.
You know who else is on an empire gradient? North Korea. Afghanistan. Belarus. You're not even specifying which side of the empire gradient. Maybe being on the authoritarian, communist side did not work out so well for many countries?
I think what matters for South Korea is moving steadily toward more democratic governance, embracing capitalism, and proximity and historic ties with Japan (not always pleasant, obviously, but ties nonetheless) at a time when Japan was developing robust trade with the US and when Japan's own consumer sector was booming, providing another market for Korean firms.
Korea has absolutely followed the pattern of moving steadily up the value chain, for example in consumer electronics, in autos.
