No.
The "firearm" in question is either a pistol-grip-only "shotgun" that the ATF classifies as "firearm/other" on the 4473 form, or it's an NFA AOW "smoothbore pistol", like a Serbu super-shorty, and if it can use a Sig Brace without being classified a NFA Short Barreled Shotgun. In this instance, it's a Black Aces Tactical Serbu Super Shorty clone, but built off their Mossberg 500 clone receiver that takes Saiga 12 box magazines.
At this point, the tech branch letter has nothing to do with pistols, AR, AK, Sig 55x types, etc. as the GCA, NFA, or the ATF defines the term.
And "in before" someone cries "dupe" on this. Although ar15.com is not particularly searchable, because it would kill the board's database performance if it were. The real trick is to go to google.com and put in "
ar15.com: what-it-is-i'm-searching-for" and you might find it.