I consider myself a nihilist, and I don't agree with your description at all. I think your concept of nihilism is different from that which I hold, though. And lucky for me, I never mistook my wife for a hat, though I did read the book. It was an eye-opener!
So glad you asked ...
"extreme skepticism maintaining that nothing in the world has a real existence" ... taken from the Internet
So are you so skeptical as to be self contradictory? That definition would mean a nihilist doesn't only deny all belief, but all demonstrated fact. See the various definitions of realism and anti-realism under ...https://en.wikipedia.org/wiki/Anti-realism
Realism is classic Platonism/Pythagoreanism vs Mathematics, where proof is about things that are real, but outside our human reality, or classically objective
Antirealism is post-classic vs Mathematics, where proof is the real, not about something else that is real, so not outside human reality, but still objective
Phenomenalism is radical empiricism vs Mathematics, where all facts are driven by sense data (Qualia), but outside our human reality
Antiphenomenalism is postmodern empiricism vs Mathematics, where all facts are within the context of human experience, including but not limited to, the post-processed sense data (post-Qualia)
I am an antiphenomenalist. So I am not a classic theist or deist ... who would have been realists ... though Anselm and Aquinas would be close to antirealists. A phenomenalist would be an atheist driven by empiricism that "there is no god" vs an atheist driven by rationalism that "there is no god" ... the former saying ... there is no god in my empirical experience, the latter saying ... there is no god that is a coherent idea. My organon is that G-d is an undeniable empirical experience, but that empirical experience isn't coherent anyway. Psychologism is the term used by Wiki ... for what I call antiphenomenalism.