Nietzsche's about as far removed from Japanese and eastern philosophy as you can get. (EDIT: Although his works do appeal to many thinkers there, Keiji Ni****ani for example, but they tend to read more what they want out of it and use it to form/support a great many notions that Nietzsche himself would likely disagree with. But then that's come up a lot with him as a thinker - he also "inspired" a lot of right-wing German militants, anti-semites and nazis... They made very selective use of his work. Of course it's not exclusive to him either, let's not forget the previous administrations attempts to use the works of Orwell, primarily 1984, to discredit liberalism, despite Orwell's own political leanings.)
I mean, he had less issue with Buddhism which he saw as relatively progressive a religion (for a religion...) but that's about the closest you could tie the two together. And Buddhism hasn't been the dominant Japanese religion since before feudalism. Social Darwinism started to come in with growing English and French influence in the late days of Modern Japanese thought... but that's not really what people think of when they think of Japanese existentialism.