Yes, but I think that the reason why needs to be drawn out, because, especially after the Enlightenment thinkers, with their preoccupation in making philosophy adhere more to the rigor of mathematical arguments, it's not self-evident that he seems to be a philosopher.
Consider this more a tl;dr than a thorough argument itself; that shit would take too long.
1) Nietzsche, for all his complaints about Plato, does grant that Plato is a legitimate model of philosophy, and he in certain ways does similar work in his books. He takes it that philosophy values questioning, and not just merely answers, and in this agrees with Plato's characterization of philosophy in the Symposium as Eros (longing, desire) for wisdom. So his skepticism and effort to call into question "truths" taken for granted are both in the spirit of Plato. Practically, he's trying to put his readers in the position of questioning their received opinions. (His notebooks, on the other hand, especially earlier ones, show him privately working out hypotheses he just declares in his writings; he basically hides his work.)
2) He seems to also agree with what he takes Plato to be doing; to be, as a philosopher, a skeptic, but as a writer for readers who won't necessarily be philosophers, to present a teaching or dogma to. (This relates, not incidentally, to his criticisms of Plato and the Good and immortal soul.) But by the by, this is the meaning of what he says in Beyond Good and Evil when he says true philosophers are legislators; they present a comprehensive way of understanding the world that people might subscribe to, even if they're not strictly true. In his journals, he admits to writing "with a mask" and using bombastic rhetoric that he feels is appropriate to the situation he's addressing. It's worth doing a quick word find in Beyond Good and Evil for his only two uses of "Dionysus", which he uses to imply he and Plato are both closer than his initial argument makes clear.
3) All this puts him squarely more with the Greek philosophers than anyone after them. Parmenides laid out his thoughts in a poem mimicking Homer's style. Heraclitus wrote short passages using wordplay and puns. Empedocles and Anaxagoras use love and strife to describe material processes. Plato wrote dialogues obscuring what he believed from what Socrates believed. Etc. Nietzsche's literary style is meant to do similar work, alternately inspiring and obscuring what's going on.
I'm not sure this helps *much*, but maybe it helps to begin situating him?