u/DisFantasy01

Or are they more original?

Google says the first game is based on "Arkham Asylum: A Serious House on Serious Earth" a 1989 graphic novel that explored the mysterious and mystical history of the asylum. "Arkham Knight" seems like an adaptation of both "The Killing Joke" and "Under the Red Hood".

I haven't been able to determine if "City" and "Origins" are based on any comics, though maybe Origins very loosely follows Bane's original storyline.