In China they link the ID to a phone number (via mobile carriers) and the online services require you to authenticate using the phone (SMS etc.) Unless the kids are able to secretly access the parent's phone there's no low-effort way to work around the system.

I don't know about Korea but if memorizing an ID number works, then that's just a badly designed system.

I'm not sure what your argument is really, unless you're saying there's technically and absolutely no feasible way to securely verify the age of a person before allowing them to access an online service (even if you allow the government to be authoritarian)

Maybe it does work exactly as intended. It gives parents more leverage to restrict their kids gaming but many parents just don't care. And it's ok I guess, the society probably needs some flexibility in raising the next gen.