level, in the country, manor, village, hamlet
庄 centers on a flat, rural settlement: a level area in the countryside, a manor, village, or hamlet.
庄 combines 广 (building or shelter) with 土 (earth), suggesting a dwelling on level ground. The exact historical development is uncertain, but the component combination fits the rural settlement meaning.
Under a broad shelter 广, there is flat earth 土: a level manor in the countryside.
For ショウ, imagine the lord of the manor putting on a show for the villagers: show -> ショウ, and the whole hamlet gathers on the level ground.
—
village headman (esp. in the Kansai region)
menko; children's game in which thick circular or rectangular cards are slapped down on the ground to overturn other cards
shōya-ken; kitsune-ken; game similar to rock, paper, scissors, played with hand gestures representing a fox, hunter and village headman
village; countryside; country house