Higurashi When They Cry Hou - Ch.6 Tsumihoroboshi recently released as the sixth chapter in the series and they all have Linux support.
From what I understand, they're slight remasters over the original versions. They include both English and Japanese text as well as the option to choose the original or the updated character sprites. The series has been popular with both users and critics, to the point that it has both Manga and Anime adaptions. So to have the games on Linux is quite a treat it seems!
See for yourself what it's all about in the below trailer, likely NSFW due to girls in underwear: