Korean universities Teaching Jobs

I don't know about the document you're referring to, but I know that a Master's will make you more employable. Particularly as Korean universities are already planning or making cuts in their staffs (including professors) and programmes (majors/courses).
If you want to teach English, an MA or MEd in English, linguistics, applied linguistics, or TESOL/TEFL would be most valuable, I believe. I know some people who only have Master's degrees and teach in other subjects at universities, but I think these jobs will become rarer as well.
This is mainly speculation, of course, but I know for a fact that cuts are happening or coming in a number of Korean universities because of the decline in the birth rate which will lead to reduced enrollments by somewhere between 2017 and 2020.

I agree with Mathew that uni positions will soon be hard to come by, and already have become quite competitive. Our university has already added a requirement that candidates need two years teaching experience at the university level in addition to an MA, and we are still flooded with qualified applications. Currently, an MA via a distance program can be sufficient, but preference is still given to those who get MAs through traditional programs.

As I have come to understand things, a master's degree is required for advancement into the professor rank (E-1), however, one may still be hired by a university at a level below that, e.g., an instuctor under an E-2 visa. The greatest asset for an entry level hire is not always the master's degree but rather university equivalent years of experience. Once a person has at least 2 years of experience they may seek a teaching position at a uni. Unfortunately, univeraities do not include hakwon experience when calculating the required years of experience a candidate has at the time they apply for a professorship. Hakwon experience is included in the calculation of required years toward an instructor position though.
This blog has run a series of interviews that you might find helpful. http://www.alienteachers.com/1/post/2013/05/ma-tesolapplied-linguistics-interview-1-with-tyson-seburnt.html