Is Nietzsche a nihilist?

Is Nietzsche a nihilist?
A nihilist is a man who judges of the world as it is that it ought not to be, and of the world as it ought to be that it does not exist. According to this view, our existence (action, suffering, willing, feeling) has no meaning: the pathos of 'in vain' is the nihilists' pathos — at the same time, as pathos, an inconsistency on the part of the nihilists.

—Friedrich Nietzsche, KSA 12:9 [60], taken from The Will to Power, section 585, translated by Walter Kaufmann