First, check out what we have to say in "Classic Plot Analysis." You'll see that Chekhov wasn't one to play by the rules, at least when it came to the traditional structure of a short story. Rather than build a narrative with a typical beginning, conflict, climax, and conclusion, he creates a world that extends beyond the limits of the page. Gurov starts before "Lady with the Dog" begins, and he and Anna continue long after it ends. Chekhov's ending couldn't be farther from a conclusion. Just look at the final paragraph:
And it seemed as though in a little while the solution would be found, and then a new and splendid life would begin; and it was clear to both of them that they had still a long, long road before them, and that the most complicated and difficult part of it was only just beginning. (4.22)
So sure, Chekhov's story may be unusual, given the classic expectations for a short story, but it does other very interesting things. First, it adds a lot to the realism of this piece. In case you hadn't noticed, in real life, things just happen. They tend to not occur in episodic little pieces that can be broken down into seven stages. "Lady with the Dog" also does something Chekhov thought literature should: ask more questions than it answers. This is certainly true of the ending, when the reader is left to speculate on the future of these two lovers.