Giving a terse nod and slight bow, Fukui strides through the windowless basement chamber, passing a wall displaying editions of the GT, Kayano, and Gel-Lyte series, Asics’ flagship best sellers, stretching from the 1980s to the present. Opposite the wall of newer models, Fukui turns to a vault containing the company’s older shoes, ones with historical significance. He unlocks and wheels open a heavy air-trap door, the kind used in banks and museums. Stepping inside, now resembling a sommelier searching for a rare vintage, he scans the neatly arranged shelves of cardboard shoe boxes stacked floor to ceiling. He pulls down a box and, cradling it with both hands, delivers it to a display table in the front of the room.Fukui lifts out a pair of Tiger Runspark track racing flats. The royal blue of the nylon uppers remains vivid, as do the intersecting pairs of curving white stripes, the distinctive logo designed by Mr. Onitsuka half a century ago. The sole and midsole, however, are starting to flake and discolor with age, lending the patina of a relic. “Lasse Viren’s racing flats,” Fukui announces. “The ones he wore when winning the gold medal in the 10,000 meters at the…