It doesn't fall under the definition of a short barreled rifle or shotgun, however, it may fall under the definition of a destructive device.
Subpart B-Definitions
§ 179.11 Meaning of terms.
Destructive device. (a) Any explosive, incendiary, or poison gas (1) bomb, (2) grenade, (3) rocket having a propellent charge of more than 4 ounces, (4) missile having an explosive or incendiary charge of more than one-quarter ounce, (5) mine, or (6) similar device; (b)
any type of weapon by whatever name known which will, or which may be readily converted to, expel a projectile by the action of an explosive or other propellant, the barrel or barrels of which have a bore of more than one-half inch in diameter, except a shotgun or shotgun shell which the Director finds is generally recognized as particularly suitable for sporting purposes; and (c) any combination of parts either designed or intended for use in converting any device into a destructive device as described in paragraphs (a) and (b) of this definition and from which a destructive device may be readily assembled. The term shall not include any device which is neither designed or redesigned for use as a weapon; any device, although originally designed for use as a weapon, which is redesigned for use as a signaling, pyrotechnic, line throwing, safety, or similar device; surplus ordnance sold, loaned, or given by the Secretary of the Army under 10 U.S.C. 4684(2), 4685, or 4686, or any device which the Director finds is not likely to be used as a weapon, or is an antique or is a rifle which the owner intends to use solely for sporting purposes.
Somehow, I don't think the Director will classify it as a sporting weapon.