I think Korea will put taxes through crypto exchanges. So it means every Korean crypto exchange will required KYC and that will be the basis of Korean government because they can't put taxes to individual person because cryptocurrency is decentralized and government has no control on it. It means there is a transparency between the Korean government and to all crypto exchanges on their country.
I have accounts with several of the Korean exchanges, and I can say that KYC was already mandatory for these exchanges even before the new law was passed. In both Japan and South Korea, the regulation is quite strict and they want to make sure that no money laundering activity is conducted through the exchanges using either cryptocurrency or fiat cash.