In-universe, it's the modern day interpretation of the original Shadow Games which involve summoning manifestations of the Soul to duel each other in place of the magician/summoner. "Monster" would have been Pegasus's modern day interpretation of the original "Dueling Monster Spirits", probably chosen to be more evocative of the kind of strange and terrifying creatures that exist from this Shadow World populated by both good and evil spirits representing the life energy of everything from the sand to the Pharaoh himself. You could argue that "Summon" would be an appropriate substitute as a noun, but "Monster" was probably chosen to be as obvious as possible that it's not meant to be anymore "real" than the magic spells and traps supposedly being slung around in-game.