A quick look at their website, at the gallery for the paradox guns, I see smooth bore shotguns with rifle sights and optics mounts.

A dude can make specialty ammunition and regulate a smooth bore gun for that ammunition, but that doesn't make it a paradox gun.

I've seen this fellow's marketing flash once or twice in the last year or so, but otherwise I'd never heard of him before and I don't know where he's coming from. At the very least it looks like he's modifying old shotguns and he's loading bullets in long brass cases.

I can see how that might be confusing.

Also.
There is no "regulation point"
Properly regulated SxS rifles send their groups out in parallel trajectories.