[skolskoly]

Yeah I was a bit taken aback when reading that part and became increasingly concerned that the author didn't know what he was talking about.

Imagine your friend asks you to count the windows on a building, so you count the rows and columns and multiply them. When he asks you how you did it so fast, you tell him, and he responds with something like: "Oh, I didn't realize you were a Nihilist." He then explains that mathematics is immaterial, and therefore non-existent. You believing in such a thing apparently makes YOU the Nihilist?

No. Nihilism is not about holding supposedly "empty" beliefs. If anything, it's the opposite; Nihilism would hold that these beliefs in the immaterial are themselves empty. Your friend might be a Nihilist, but you certainly aren't.