With one eye on her baby in a stroller, Minae Kamata operates an arcade machine in a Tokyo suburb, manipulating a claw to grab not a stuffed toy but a pack of toilet paper. As inflation weighs on Japanese households, huge arcades on the outskirts of major cities are installing claw machines filled with eggs, rice, laundry detergent and other necessities. The “shop-and-play destinations” merge essential buying with entertainment so that families do not feel a choice between bringing home the...