It's hard to know who's to blame for this. The South Korean government has been championing a clampdown on access to explicit materials such as online porn (via proxy through Christian groups), but at the same time, it's hard to think that these same prudes have actually spent much time listening to early 90s American hip-hop or Swedish rock. More likely, Youtube (and by extension, Google) are now suggesting that perhaps certain songs are best heard by mature audiences, and whatever boolean switch got flipped there meant that if you're in Korea, you've now got to to prove you're old enough to hear such dangerous material.
This is the page you're sent to in order to verify your age for the Wu Tang video, although the TLD ageverification.google.co.kr doesn't take you anywhere. Entering false information to circumvent this bullshit leads to an error message saying "Your phone information is mismatched." which suggests that Google is working with South Korean telecom companies to facilitate the censorship.