We mean that his native language, not one that he's acquired subsequently, but the one that he learned as a child, was Greek, some version of the Greek language.

我们以他的母语为依据,即他们非后天习得的,而是从小所学的语言,即是希腊语的,或是一些希腊地区的方言的

耶鲁公开课 - 古希腊历史简介课程节选