Just a thought, since it has a pistol grip and no shoulder stock, it would be a pistol, just like any thompson contender that fires shotgunshells or rifle cartridges.
I have a super 14 contender and the paperwork in Delaware is the same as for a pistol.
Except your T/C still has a rifiled barrel. That is how they are able to do it. The Super Shorty has a short smooth barrel and that is where the rub is.
Anyone who could shoot a perfect round of skeet using that thing and high brass turkey loads would be summarily granted "God of Manly Things" status. Hmm... see a competition coming up. To be shown on ESPN right after "World's Strongest Man" competitions