There are several parts to this question. The first is why it had more influence on Japanese art and, arguably, society than Pure Land Buddhist sects such as Nichiren which have always had more adherents. The next question is why that is also true of those sects’ influence abroad.
The main reason Zen had more influence in Japan was that it was the sect of choice of the samurai class who controlled society, whereas Pure Land Buddhism generally appealed more to ordinary people. Aesthetic appreciation was also more a part of Zen than other sects, hence its outsized influence on the arts. Both of those aspects are relevant to its reputation amongst foreigners, many of whom were upper class aesthetes who were naturally attracted to the minimalist, subtle upper class Zen-influenced art.