So... is Ousama Game The Animation finished or not?
NO, it is not finished.
Why?
The anime finished after the manga:
Anime finished: December 21, 2017
Manga finished: January 25, 2016
... But MangaUpdates contains information about the anime adaptation and indicates that it is incomplete.
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
Nobuaki Kanazawa, a student with a troubled past, transfers to a new school with the intention of keeping to himself. However, his plans are disrupted when the entire class is forced to participate in a deadly game orchestrated by someone calling themselves "The King."
The "King's Game" involves receiving increasingly bizarre and dangerous orders via text message, with severe consequences for those who fail to comply. Knowing the horrors of the game firsthand, Nobuaki attempts to warn his new classmates.
As the game escalates and the stakes become higher, Nobuaki is faced with a difficult choice: protect himself or try to save his classmates from the King's cruel and deadly commands. He must overcome his past and decide how far he's willing to go to survive and potentially help others.