According to what is written, you are likely correct, Socrates. Yet when I accidentally made the reservation and called to cancel, I was told exactly what 1P writes.

Bottom line: It is horribly written. Based on what's written, the OP should be entitled to a refund if requested at least thirty days out, but would likely find resistance from the hotel based on what I was told when I called. Better the OP should NOT call and ask, so as to save the "confusingly written" defense if he needs it than to have the hotel give him their interpretation now, making it harder to claim confusion if the defense is needed later.