supernatural events

I believe he imagines them. The language of The Queen of Spades, to me, is highly metaphorical, and the ghost and other events seem to be his slow descent into insanity, rather than the supernatural events occurring externally of his perception.

On the other hand, if we take the world presented at face value, supernatural events do seem to occur regardless of the perception of the main character: the "secret" of the cards seems to work, as the countess was able to dispense with her debt, and it did work for the main charactter until the queen "haunted" him in the game. I think it's difficult to say whether the supernatural events actually happen or whether they are imagined.