They put down a stone and throw at it from a distance with balls or pebbles. The one who fails to overturn the stone carries the other, having his eyes blindfolded by the rider, until, if he does not go astray, he reaches the stone, which is called a dioros.
Children in antiquity played ephedrismos, the game the ancient Greek writer Pollux describes above and which is pictured on this lekythos. Although this looks like a scene of children at play, the two figures represented here are actually a satyr--identified by his beard and the hint of a tail--and a short-haired woman called a maenad. Both satyrs and maenads were followers of Dionysos, the god of wine, vegetation, and the theater. Satyrs and maenads cavorted in a childlike manner, so it is not surprising to see them playing this version of a piggyback game.
Lekythoi like this one were tall flasks that held precious oil that was used in funerary rituals. The vessels were then left on the graves or buried with the deceased.