The answer is pretty simple, because das explicitly doesn't refer to the nose that was in context. This "das" is an indefinite pronoun and thus does not receive a gender, but defaults to neutral, inanimate gender. We might also use "dies", "es", or even "so-etwas" ("Sowas ist doch nicht normal").
If talkling about people instead, we would make a difference, "Nein, Sie ist keine Nase", and we might use gendered articles as pronouns, too, e.g. "die", shortened from "die Frau", or "Der ist so schlau, der vectory".
We only refer to a specific gender, if it's already in context, but it just doesn't work well with negatives. Hence:
Das ist gar keine Frage
Das ist ja wohl unerhört
Vice-versa, we may use the indefinite pronoun for positive statements, pretty much by analogy
Ja, das ist ein Golden-Retriever
Which is unproblematic because in most cases we could surmise a neutral noun to fit, e.g. "das Tier".
dies seems to be a mix of both die and das, in case you can't decide :) but we also have the anaphoras "dies und das", and "dieses und jenes".
es actually stems from a meaning "here".
Combining both we get dieses ist keine Nase (which sounds a bit like ellipses of dieses Ding). We would not say diese (female) in such cases, however.
etwas--I found nothing concrete about it--may by my estimate be in part from es, PGmc *hit "that", PIE *ke-, *key- "this, here", too, bound with "was" cp. "Ich habe hier etwas", "look at this here".