So... is Rio: Rainbow Gate! finished or not?
NO, it is not finished.
Why?
MangaUpdates contains information about the anime adaptation and indicates that it is incomplete.
Watching Order (by release date)
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Synopsis
Rio: Rainbow Gate! centers around Rio Rollins, a popular and skilled casino dealer at the Howard Resort Hotel known as the "Goddess of Victory".
Rio aspires to follow in her mother's footsteps and become a legendary dealer.
To achieve this, she must collect thirteen special cards called "gates" scattered throughout the resort.
Gathering all the gates will earn her the title of MVCD (Most Valuable Casino Dealer), proving her to be the best.
The story follows Rio as she competes against other talented and alluring dealers in exciting casino battles, all while navigating the vibrant and sometimes unpredictable world of the Howard Resort Hotel.