When the text is in Korean but not in Korean.
TL Notes
Note that there's a very pronounced "-gu/-geu" sound in the first speech bubble, similar to how English speakers would call King "Kingu" to approximate the JP pronunciation. This is then followed by -jjyang, which is one way of rendering Japanese -chan in Korean.
Second speech bubble is Kingu going "Mou!" with a very dragged out final syllable for added exasperation.
Updated