The dilemma is not man versus himself because Iona is aware of the source of his misery. A personal dilemma would have placed Iona in a position where he battles against an obvious cause that he tries to deny.
Neither is the dilemma of a man versus man nature because there is nobody else challenging nor discrediting Iona's emotions. There is, in fact, no man at all for him to speak to. It would be hardly a man versus man issue.
The main conflict, or dilemma, in Anton Chekhov's short story "Misery" is that of man versus society.
Main character Iona Potapov is a cab driver (horse cab, that is, as the story is set in the 1880's) whose son dies that same week. Unfortunately, life must go on for Iona. Yet, we realize as the story goes on that Iona is alone in the world, and has absolutely nobody to speak with and let himself vent his sadness.
All that he can do is try to convey some of his emotions to an officer who takes the cab to Vyborgskaya. However, as he tries to explain his sorrow, the officer's attention goes back to the eagerness of getting early to his destination.
As more people enter the cab and abuse the driver's inability to concentrate, he finally finishes his rounds only to see that, he cannot even count on his own peers as a support system. As a result, he ends up talking to his horse.