"As an online discussion grows longer, the probability of a comparison involving Nazis or Hitler approaches 1."
Of course it applies. It's an online discussion, and a comparison was made.
And your claim that a meme doesn't apply to something just because it wasn't in the exact same context as its first use means you clearly don't understand what a meme is in the first place...
If you're not satisfied with his answer, I can provide another for you. I don't think you really need to have this explained to you. I think you just wanted a simple, lazy, effortless slam-dunk "victory" so you can congratulate yourself for ending the thread. Continuing...
For one, mentioning Nazi Germany is perfectly valid when the topic is government power and how it incrementally escalates beyond control. It's just a fact that forcing gun owners to register their firearms made it a simple matter for Hitler's government to confiscate them. It's also a fact that dictators commonly take guns away from law-abiding citizens prior to becoming despotic. Most (all, I hope) people don't want to live under a brutal dictatorship, dictators know this, therefore dictators want the citizens to be as helpless and powerless as possible.
Godwin's law applies especially to inappropriate, inordinate, or hyperbolic comparisons of other situations (or one's opponent) with Nazis. The law and its corollaries would not apply to discussions covering known mainstays of Nazi Germany such as genocide, eugenics or racial superiority, nor, more debatably, to a discussion of other totalitarian regimes or ideologies, if that was the explicit topic of conversation, since a Nazi comparison in those circumstances may be appropriate, in effect committing the fallacist's fallacy.
"Genocide, eugenics, racial superiority ..." would reasonably include how a government becomes powerful enough to implement such horrifying policies.
Also from Wikipedia:
This principle is itself frequently referred to as Godwin's law. It is considered poor form to raise such a comparison arbitrarily with the motive of ending the thread. There is a widely recognized corollary that any such ulterior-motive invocation of Godwin's law will be unsuccessful.
That would apply to you.