See your take-home amount after withholding tax
Yes, that can happen. Prizes of 2,000,000 KRW or less are entirely tax-free, but cross that line by even 1 KRW and tax applies to the whole prize, not just the excess. A 1,999,000 KRW prize can leave you with more cash than a 2,010,000 KRW one after tax.
It is a progressive split: 22% applies to the portion up to 300,000,000 KRW, and only the amount above that is taxed at 33%. The whole prize is never taxed at 33%.
In most cases, the withholding tax is final (separate taxation) and no additional filing is required, aside from unusual situations such as multiple large wins in the same year. Check with a tax professional for your specific case.