I do want to apologize cause it seems like there may have been some confusion as to our current offering of .kr, .ne.kr, .co.kr & .re.kr registration; which we do offer as indicated on the help article link you referenced.
You should be able to search for any of these domains on our registration page. Just type the name you'd like with the full extension to see if it's available. Do be aware of the requirements that state "If you live or work in Korea, please provide your registration information in both English and Korean. Businesses or organizations must also provide their Korean Business License number."
CG - GoDaddy | Community Moderator 24/7 support available at x.co/247support