That's what made the movie famous & remembered.
Legend has it that McQueen did his own driving. That's not entirely true but he did more than most actors. They hired a stunt driver to play that hit man driving the Charger so he really did it all himself.
They filmed that whole movie with only two copies of each car, one stunt and one closeup. The Mustang gets all the press but in reality the film crew said the Dodge Charger was absolutely kicking the Mustang's butt, both outrunning it and withstanding more punishment.
That chase still looks good today but it was absolutely mind-blowing in 1968. Nobody had ever done anything near that before. The totally real world setting, the well-photographed action, the cars really going fast without too many camera & editing tricks, no blue screened or projection backgrounds for the in-car shots, etc.