Proulx keeps the story in the realm of realism, even though it's fiction. Everything adheres to the tenets of reality, nothing happens that we wouldn't expect in the natural world, and we could very easily see this scenario taking place in the actual world (unlike, say, Harry Potter, where as much as we would like to believe the Hogwarts is out there somewhere, it just isn't. Trust us. We looked.)
Proulx tinges the realism with shades of Romanticism with a capital R, referring to an 18th-century movement that tried to understand the natural universe through human perception. You can see shades of it in the descriptions of the landscape, in Ennis's heartbreaking emotions, and in the way the two seem to twist back on each other more than once.