Yeah... the book and movie predate the Chernobyl disaster and have nothing to do with it. The Chernobyl connection is something the game's creators made up because of the superficial similarities (an exclusion zone where traces of human civilization are still visible).
In the book, the Zone is one of a handful around the planet, the sites of a brief alien visitation where anomalies and weird stuff happens. The book's name, Roadside Picnic, is a reference to a metaphor that scientists have to explain the Zone - as if a family on a road trip stopped to have a picnic, then went on its way, and left its litter strewn all about the place, for the local nature to deal with. By the end of the book, humanity has actively embraced Zone technology - they have electric cars powered by self-replicating Zone batteries that never lose charge, for example.
The magical stone at the center of the Zone that grants your deepest darkest wish is from the book. The main character is a stalker who brings artefacts out of the zone to sell, like in the film, but he's a family man, and when his child is born with a mutation caused by his exposure to the Zone, he plans a trip to the magical wish-granting stone to cure the child. He is forced to do some straight-up evil shit, intentionally causing other people's deaths, to get to the stone, and when he gets there, he is incapable of formulating his wish, screaming at the stone, "You are supposed to be all-knowing and all-powerful - look into my head and figure out what I want! Peace and happiness for everyone, forever, for free!"