No, there were books, then there were games. The games changed some stuff (probably, didn't read the books didn't play the games didn't watch the show), the show changed more from the games.

The books were an original idea, but there were a few of them before it got notable enough. Point is the showrunners aren't pitching original ideas that immediately shoot to popularity, original shows need time to build up to know if it's good but networks and publishers can pull the plug anytime they decide it's not fast enough. You don't strike gold on the first 3 episodes.

Let’s simplify:

Writer X has an idea for a fantasy show

Can’t get it sold

Writer X slaps Witcher lore on their own script loosely

Script is sold because now it’s a known property, the industry likes that

Now the writers follow the “official” plot for a while and steer towards their own ideas more and more because that’s what they wanted to do originally.