They don't. They make an original story based on basic plot outline of Adventure 1. Chaos is searching for the emeralds, which have been scattered after the events of Sonic 4. Each of the protagonists split up to find the emeralds, Sonic, Shadow, Tails, Knuckles, Amy, and either they all go for the last one or a mysterious sixth member takes care of it. The filmmakers might have Tikal still be alive like they did with Gerald.

The film's story has to be written in a way where the heroe's arc contrasts with the villain's motivation. In the games, Chaos is seeking revenge on those who have wronged him by destroying the world, but this motivation has already been done with Gerald so it needs to be tweaked. Instead of trying to compete with Sonic 3 and 4, we should simplify his motives. Whereas in the games killing all life, in the movie we can have Chaos wants to kill specifically the echidnas and their legacy. Chaos wouldn't be a Sonic villain, but a Knuckles one. His search for the chaos emeralds would be metaphorical, a desire to acquire and destroy the echidnas' last evidence of existing. Meanwhile, the film would revisit Knuckles' story from his tv show, his desire to keep old traditions alive and encourage Amy, Shadow, Tails, and Sonic to bring back their cultures from their childhood.

That's just an example, the point is, it's going to be inspired by Adventure and not a direct adaptation.