The books rather inspired the games - or their developers - and weren't really a previous story.
But what about the series?
Do the screenwriters or the director make any claim that the plot of the series is the history of the games?
Seen in this way, the games and the series have no connection to one another. The series is closer to the books and the games are not.
The game takes place after the storyline of the books (and makes enough reference to it), and the storyline follows the books and short stories, as the makers of the series said. Therefore, yes, the series is very roughly the prehistory, whereby the series, as usual with something, takes the freedom to deviate from the books here and there.
