While the story does focus largely on Gurov, his perspective, his thoughts, and his story, the narrative voice of "Lady with the Dog" is allowed total omniscience. Check out the story's final scene. First, we're given access to Anna's thoughts: "She was crying from emotion, from the miserable consciousness that their life was so hard for them; they could only meet in secret, hiding themselves from people, like thieves! Was not their life shattered?" (4.11). Then, we jump back to Gurov's perspective: "It was evident to him that this love of theirs would not soon be over, that he could not see the end of it" (4.13).
There are also moments in the narrative when we seem to get commentary from this formless third person narrator, outside of both characters. Consider this somewhat perplexing passage:
The leaves did not stir on the trees, grasshoppers chirruped, and the monotonous hollow sound of the sea rising up from below, spoke of the peace, of the eternal sleep awaiting us. So it must have sounded when there was no Yalta, no Oreanda here; so it sounds now, and it will sound as indifferently and monotonously when we are all no more. And in this constancy, in this complete indifference to the life and death of each of us, there lies hid, perhaps, a pledge of our eternal salvation, of the unceasing movement of life upon earth, of unceasing progress towards perfection. (2.28)
Is this the commentary of the narrator, or are we slipping into Gurov's mind here? It's not exactly clear. Check out the context – the lines before and after this passage – and see what you think.