I wouldn't pretend I know the exact difference between manga and doujinshi, but this is definitely not Manga. Doujinshi doesn't always use pre-existing characters, but manga never does. Also, nobody actually has sex, so this could be Non-H. And if this is a commission, that sort of implies this was made by a Western artist, for a western author. This could be wrong, but whatever the case, this comic should definitely not be listed as a Manga.