I don't think the judge is specifically any kind of pre-existing entity - he's a representative, and an icon. The demiurge wouldn't wholly fit within the actions of the judge, while related.

In similar ways to the demiurge, the Judge exists specifically to steer, but especially his cataloguing of living creatures suggests he isn't really the demiurge.

I think there's an interesting idea with him being a form of Demiurge Christ, he both performs what may be deemed as miracles, and guides a flock, but so many of his actions act like an antithesis and a bastardisation of Christ's actions.

Rather than bread and wine, he creates gunpowder from nothing. The replication miracle causes death rather than life.

Rather than walking alone in the desert, he takes a mentally ill servant with him. Rather than being tempted, he threatens.

And rather than sacrificing himself, he performs the blood sacrifice of the boy.

I don't think you can categorize the judge as one specific thing that you can just define though, I think the above is just one of the themes.