No one claimed they have a Legion of Doom-style HQ with their version of Lex Luthor sitting on a throne.

And no one claimed that you were claiming that.

It's not an organization. It's an idea and belief system, like "environmentalism." If you tried to claim that "environmentalism" was an actual organization, rather than an idea and belief system, the fact that most organizations don't have a LOD HQ doesn't make you correct.

How did Al Qaeda work? Did they maintain a list of Secret Terrorist Operatives Hidden Around the World?

No, but they were an organization that had a leadership structure. There was a head of Al Qaeda.

Just because there are some organizations that lack a headquarters and membership list doesn't mean that everything that lacks a headquarters and a membership list is an organization. The philosophical concept of Epicurianism also doesn't have a LOD-style HQ or a secret list of Epicurians around the world - and that doesn't make Epicurianism an organization, either.

I find this Antifa denial just...fascinating.

You're using a term wrong, and it's being pointed out to you. Why is that fascinating to you?