This is ultimately a revenge story, but not a straightforward or clean-cut one; in this way I would compare it to "Memento" and "The Three Burials of Melquiades Estrada".
It's not clear who we're "supposed" to sympathize with at the beginning. We want to sympathize with the revenge-seeker; but we're told almost nothing about why he wants revenge. As he displays at least as many brutal and mercenary traits as anyone else in the film, we question why we side with him, and realize that we're only inclined to do so because our previous experience with "revenge" stories has programmed us to do so.
But the quarry is far from a sympathetic character as well, and we're torn emotionally on what we want to see happen. That is, until the original tragedy is finally revealed. And I've honestly never seen such a well-conceived scene of this type... the tragedy is heart-rending.
I won't say much more except that as the film goes on, the degree to which it will appeal to fans of literal straightforward westerns decreases significantly. You see, as the film begins, Carver's pursuit of Gideon takes them through various isolated episodes: encounters with various characters. As the film goes on, these encounters become more and more obscurely surreal; the final such encounter seems almost supernatural or fantastic. The writer and director have peeled away the internal reality of the story, and are speaking to us through the form itself. Not something that your average Western viewer is likely to accept or appreciate.
Viewers will come to this film expecting a completely realist story; and that's what they seem to be getting at the beginning of the movie. The viewer is not prepared for this realism to slowly and obscurely fall apart - and while that may be the reason that the film creates such a powerful and somehow creepy experience by the end, the same factor is likely to leave most viewers feeling robbed.
Ultimately this film is definitely worth watching, but may not have enduring appeal to lovers of the traditional Western genre. A note while viewing: pay attention to the theme of loss, and how various possessions of the characters are lost.