So... is Kizuoibito finished or not?
YES, it is finished.
Why?
The anime finished after the manga:
Anime finished: August 25, 1988
Manga finished: March 30, 1986
MangaUpdates contains information about the anime adaptation and indicates that it is complete.
Watching Order (by release date)
Here you have all the anime relations we detected ordered by release date, so you can see the reason for this status in context and also use it as watching order.
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Synopsis
Yuko Kusaka, a Japanese journalist, travels to Brazil to investigate the gold rush and find a mysterious Japanese man called Rio Baraki, rumored to be striking it rich in the Amazon.
Her arrival is met with violence, serving as a warning to abandon her investigation. Despite the danger, Yuko persists in her mission.
She discovers that Rio Baraki's real name is Keisuke Ibaraki and learns about his past: a promising athlete framed by a powerful organization called GPX.