How does the path help safari leaders control the hunters in the short story A Sound of Thunder?
Ray Bradbury's short story "A Sound of Thunder" is about time travel. The whole idea behind the story is that time travel has become possible, so companies like the one in the story have turned it into a business. This is no surprise since every discovery prompts a new wave of people who try to capitalize on it.
One of the most important theories about time travel is that nothing must be done in the past that will alter the future. The ripple effect could not be predicted so that great care must be taken to prevent any changes to the past. This is why with great care the company has built the path to the spot where the Tyrannosaurus had died naturally. Since he was going to die anyway, then shooting him at that exact moment was determined to be safest, with the fewest, and hopefully no, consequences in the future.
So that, yes, the path was built for the express purpose of controlling the hunters that they took to the path. The belief was that it gave them total control over the hunters and that they had guaranteed that there would be no problems. A belief that Scott Eckels would prove to be false.
Symbolically one might see in the path a political position that "whoever controls the present controls the future." And that this control must be exercised continually and completely, something that is impossible to do.
Bradbury was quoted as saying he didn't "write to predict the future, but to prevent it." Could this be one of those time? You decide.