Since Pushkin employs magicalism in "The Queen of Spades," it is a little awkward to identify the theme of the nature of God versus the nature of man in the story. Critics generally prefer to identity the themes as the supernatural versus man, where "supernatural" is defines as pertaining to ghosts, visions, magical secrets, and superstitions. Another common critical way of identifying the major theme is as the Greek theme of the "golden mean," which in Pushkin's story is shown as virtue versus obsession.
Having said that, if one chooses to see God as the instigator of the supernatural elements--the winning secret, the countess's winks, the appearance of the countess's ghost, her being commended to reveal the secret--then it is possible to identify a theme of the nature of God versus the nature of man in "The Queen of Spades," though it isn't a very pretty (or, some would argue, a very accurate) picture.
In this reading the nature of God would be seen as capricious (having a secret that is periodically disbursed to taunt humanity), vindictive (the wink from the Queen of Spades at the end when Hermann misses and loses all), able to intervene in the affairs of humankind at will, though not necessarily for the good of humankind (the existence of the secret to winning and the Countess's intervention in Hermann's life as a vision or ghost).
The nature of man in this reading is shown to be weak and given to vices; in need of control as Hermann controls his overpowering interest in gambling; given to obsession; gullible and with a leaning toward believing the incredible; and, importantly, perhaps not always master of one's own fate.