In the source comic we get a little more commentary on the 'oldest game'.
The aim isn't just to say words, it's to embody them with your whole being. Dream doesn't just say "A hunter, horse mounted", he actually has to "feel the grass beneath my hooves, the flanks between my legs" in order to play his go.
Dream identifies that there are several ways to lose, notably a lack of imagination. Choronzon is a certainly a puissant opponent (being one of the uppermost Lords of Hell and capable of embodying many shapes, from the smallest to the very largest) but this is a game of subtle skill as well as gross power.
Once he has the measure of the demon he leads him into a path that he knows that will result in victory.
Dream's choice of "Hope" leaves Choronzon speechless. For all his power as a demon, he has no idea how to dispel hope in others.
Dream explains to Morningstar that hope is eternal, and hence cannot be destroyed, at least not by the minions of Hell.