Which makes as much sense as possible given the circumstances for an AR pistol, but why wouldn't the pictured shotty - or any PGO shotgun - be a destructive device? Because the ATF hasn't classified them as "non-sporting" yet, like they did street-sweepers? As you noted, they aren't legally shotguns, after all...
More on the PGO shotgun situation can be found here.
(If you're in Indiana, BTW, remember that, per Estep v. State, a PGO shotgun is a handgun for purposes of carry and transportation.)
This is simultaneously the problem with regulation and the problem with changing those regulations.
Regulation serves to usually make honest people criminals (e.g., chop your shotgun barrel to 17.9" without proper permits and you're now a felon in possession of a SBS). And when regulations are arbitrarily changed and ruled on (e.g., allowing the Sig Brace to be considered legal, even though it represented a potential NFA end-run), people will push the boundaries until you have to go back to being heavy handed (e.g., the end result of this will be NO sig braces).
Assholes will be assholes. And the simple fact is you can't regulate assholes and idiots into doing what you want without taking it to the extreme. I guess the longer I think about this crap the more I realize there is no compromise. I don't support banning them all, so I come down on the side of the spectrum that is howitzers and nukes for everyone. But I'm afraid that the other side will be the end result...
Shotguns that come with pistol grips from the factory are not shotguns (which are fired from the shoulder). They also are not pistols. They are firearms. Under the law as I understand it. Firearms only need to be over 26 inches long. With a pistol grip, that requires a barrel of certain length, and 18 is easy.
If you put longer "birds head" grip on it, you can go down to a 14" barrel and still have the whole thing be over 26 inches. Again, only legal if it only had a pistol grip from the factory.
Because the addition of the receiver extension/pistol buffer tube would add more length, I can see the logic behind an even shorter barrel as the OAL would still be over 26". At that point the addition of the brace shouldn't matter either since it's not a stock.
The way laws are written, it makes sense (and I've thought about this very thing previously).
As per it being unpleasant to shoot even with push/pull, my shotgun barely touches my shoulder when I shoot, so not sure how it would do.
I could be wrong on this all, but that's MY understanding of it (again, having researched it a bit because I thought about this a little while ago and even asked about it on M4C)
Owner of Aridus Industries. Creator of the Q-DC, CROM, and other fun shotgun stuff.