The Road by Cormac McCarthy is a brilliant and haunting book. As for whether this book has a traditional structure, I would say no. To come to this conclusion, it will be important to know what a traditional structure is and then see what McCarthy does in his novel.
A traditional story has five elements - exposition, rising action, climax, falling action, and then resolution. Of course, there can be variations, but this is the basic structure of Western novels. The most important sections are climax and resolution. The reader should feel as sense of closure at the end of the story.
When we examine the book, The Road, we can see that one important element is underplayed or not fully developed. This is why the book lingers. There is no resolution. After the boy's father dies, he is taken in by one of the "good guys," but there is little sense that they will make it. To put it another way, they are still on the road. A traditional ending would have an end to the road, which this novel does not have.