In an era with little to speak of in terms of amusement, children were nothing but excited when entertainers came by.
The yama children
"Carrying down the lanterns from ages seven or eight, down into the mines – mom and dad's punishment, clang!" In the Meiji era, if their parents got sick or were injured and couldn't work, children barely old enough to be able to ask for a snack would take off from school to help out around the house and go down into the dark mines to assist in whichever way they were able.
Some would babysit the younger children, and others would push coal carts. They would help their busy parents regardless of circumstances, picking up pickaxes from the smith that had been sent out to be sharpened and carry them home, drawing water, collecting firewood, and cleaning lamps. One could not help but feel sorry for the children in a household whose parents were bedridden for any period of time.
When electricity became available and children didn't have to clean lamps anymore, they were probably even more excited than the grown-ups were.
Boys and girls playing hide-and-seek together
As for games, boys played pattchi, a children's card-flipping game (also called menko, pattchin, or buchiko), chikuba (walking on bamboo stilts), horse-riding (the "rider" sticks out some fingers while his mate closes his eyes and tries to guess how many; if he gets it right, they switch roles), top-spinning, kite flying, nenbo (a match in which one's opponent tries to knock over a stick stuck in the ground), playing soldiers (imitating the Sino-Japanese and the Russo-Japanese wars), kosan iwase gokko (lit. "make them say 'surrender'"), jijo tori (lit. "taking territory"), fishing, and catching loaches. Girls played games like jump rope, ohajiki (a marbles-like game played with small glass discs), beanbags, holding hands, ishikeri (hopscotch), and bounce-the-ball.
Of course, sometimes boys and girls would play together as well, with games such as hide-and-seek and "carp climbing the waterfalls" (children face each other and make a platform by locking their hands and arms together, and let another child lay down on top, jostling them about like a fish on the waves). And of course the children would gather in crowds whenever a peddler or entertainer came around, as it was an era in which amusements were not so common.
Children especially loved the horai mame vendor (this particular merchant would go through the town doing a goofy dance while striking his drum, peddling his candy beans), Inari-sama (a merchant who would use a wind-up white fox to tell fortunes), the ochini medicine peddler (a person who would sell medicine while playing the accordion and giving origami balloons and things to children at no cost), the bun-mawashi game (one spin of the wheel for one sen; if the needle stopped on a winning section of the wheel, the player won a prize), and the hobby horse folk that came around New Year's (travelling entertainers with papier-mâché hobby horses who went about dancing and singing to the rhythm of bells and clappers).
The boatmen naturally resented this: "Dang land-steamers [trains] knocked the rice bowls right outta our hands. Knocked 'em right out."