Kirk here. This article says that the Ministry of Education is pushing public high schools to create special entrance exams etc. for foreign students to make it easier for them to continue their education. Kumamoto is one of the prefectures in that is in compliance. The prefectures in light green have not made a special entrance exam system to help foreigners but conduct interviews with individual students wishing to study at a high school (presumably, in lieu of an exam). The prefectures in grey are not taking either type of action to accommodate foreign students.