It's unimportant whether or not supernatural events occur, the important thing is that Hermann is confined to a mental hospital. The reason Pushkin's story lacks all subtlety is because it exists in service of a hoary old moral: greed and ambition lead to ruin (roughly). As Hermann pursues the secret of the three cards (i.e. wealth) he disappoints a woman who is at least somewhat enamored with him, becomes complicit in the death of an old lady, and ends his life in a kind of monomania (picturing people as cards, repeating sequences of cards etc.). For these improprieties Hermann is punished, whereas Tomsky, who abstains from the search, is promoted. Clearly Pushkin the moralist is trying to tell us something.