So... is Arcade Gamer Fubuki finished or not?
NO, it is not finished.
Why?
The anime finished after the manga:
Anime finished: January 25, 2003
Manga finished: January 01, 2000
... 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
Fubuki, a supremely skilled arcade gamer, aims to reach the pinnacle of the arcade gaming world by conquering the BAG tournament. Her unique ability is linked to special undergarments.
However, a nefarious organization, the Gulasic Group, is manipulating the tournament for world domination. This means Fubuki's gaming skills will be pushed to their absolute limit.
To thwart the Gulasic Group's plans, Fubuki allies herself with the enigmatic Mr. Mystery. Together, they must overcome formidable opponents known as the Gods of Gaming to protect the integrity of arcade gaming and the world.