It's very spiritual to the Japanese, yes (those who are spiritual anyway). Cherry blossoms (the flower viewing (hanami) referred to in the quote, during the sakura matsuri) is a very important cultural symbol of beauty, life and their transience, and a vivid reminder of the cycle life and death (and rebirth). Flower viewing both delight and sadden them - it's a pleasant occasion in the spring for family picnics (that turns into big parties, actually), but often tinted with introspection about life and death. Japanese are deeply attached to seasonality, but the cherry blossoms remain one of its strongest/most popular symbols (and flower viewing traditions, and its spiritual (buddhist) dimension go all the way back to ancient Japan (not the better known medieval period and the samurai, but even in Heian and Nara/Heijo periods) and has remained popular through all periods. Zen samurai were especially fond of them, both aesthetically and philosophically)

The transience and beauty of the blossoms is reflected in the seasonnal food they bring for flower viewing (beautifully and delicately arranged, especially around Kyoto, matching the beauty of the cherry trees in bloom. Transient beauty, again) Even today many have special bento boxes they use only for the sakura matsuri. The ones mentionned in the quote would have been beautifully crafted tiered boxes, likely made of
thin (almost paper thin) cedar wood, or woven of bamboo or reeds. To enjoy them and the beautiful craftsmanship and willingly destroy them after they have served their purpose instead of getting attached and trying to preserve something that wasn't meant to last more than a day is of course symbolic. The idea is that such things, like all the beauties and joys of life, have to be enjoyed at their fuellest when their time comes, and it's as important to understand they are so moving and enjoyable because of their transience, and to learn to let go.

That's far less true in modern times, people go flower viewing mostly to party (pretty much like western feastdays are for the majority more about family parties and treats than about spirituality)