For once, ATF Firearms Technology Branch actually gets one right. There is NO category of firearm which includes something designed to be fired with two hands, but without a shoulder stock.
Len Savage at Historic Arms LLC in GA is the one who received the original ATF letter.
Here is that letter:
http://www.nfaoa.org/documents/testttt20001.pdf
ATF very specifically states that a pistol-gripped shotgun with a barrel under 18" is NOT covered by the National Firearms Act. So, it cannot be a 'Destructive Device' OR an 'Any Other Weapon' (AOW) as those firearms are very specifically covered by the NFA.