It seems that this portion is relevant:
승급(18급~1급) - 최근 15국 기준 승률 65%이상(10승5패 이상) 1급수 상승
최근 15국 기준 승률 90%이상(14승1패 이상) 2급수 상승
승단(1단~4단) - 최근 20국 기준 승률 70%이상(14승6패 이상) 1단 상승
최근 20국 기준 승률 90%이상(18승2패 이상) 2단 상승
승단(5단~9단) - 최근 20국 기준 승률 75%이상(15승5패 이상) 1단 상승
최근 20국 기준 승률 100%(20전 전승) 2단 상승
So basically, it seems that, from 18k to 1k, the most recent 15 games are used as the standard. Out of those 15 games as a standard, if you have a win rate of 65% or higher (eg. 10 wins, 5 losses or more), you move up one rank. Out of those 15 games, if you have a 90% or higher win rate, you move up 2 ranks (eg. 14 wins, 1 loss or more).
From 1d to 4d, it uses the most recent 20 games as standard. Out of those 20 games as a standard, if you have a 70% win rate or higher (eg. 14 wins, 6 losses or more), you move up one rank. Out of those 20 games as a standard, if you have a 90% win rate or higher (eg. 18 wins, 2 losses), you move up 2 ranks.
From 5d-9d, it uses the most recent 20 games as a standard. If you have a 75% or higher win rate (15 wins, 5 losses or better), you move up 1 rank. If you have a 100% win rate (20 games in a row of pure wins), you move up 2 ranks.
Provided that I understood the text correctly, this seems to be the system.