Besides being only four of them, didn't Japan experience a booming economy along side the Four Asian tigers, warranting the title?
Japan was already a massive industrial economy before World War II, while the others were still relatively agrarian economies in comparison.
Japan had begun industrializing as an independent nation in the 1860s During the Meji Era.
More important the term "Asian Tigers" was coined in the late 60s when Japanese high speed growth was already cooling and when Japan was already a developped country.