In "A Sound of Thunder," why was the walkway so important to the success of the safari and the future of the world?

In "A Sound of Thunder," the walkway is crucial to the success of the safari and the world because it ensures that nothing in the past is altered. This is important because any change made in the past, no matter how small or big, has consequences for the future.
The importance of the walkway is demonstrated through its description. It hovers six inches above the ground, for example, and does not touch even a blade of grass in the past. The Safari Guide, Mr. Travis, gives clear directions that nobody must ever stray from the walkway:

Don’t go off it. I repeat. Don’t go off. For any reason!

When faced with the dinosaur, however, Eckels has a moment of panic and strays from the walkway. It is only at the end of the story that he realizes that he has stepped on a butterfly, an action which has forever altered the course of time.