Negative, Ghost rider.
Your depiction is that of weapon that appears to be less than 26" in OAL and a barrel of less than 18"; and not intended to be shoulder fired. It would never have been manufactured as a shotgun by definition, ergo, it never could be a "short barrel shotgun" in NFA parlance.
IF less than 26" OAL with birds beak styled grip it would be NFA classified as an AOW, "any other weapon", requiring NFA registration with tax stamp etc.
From the BATFE NFA Handbook:
2.1.1 Shotgun A shotgun is a firearm designed to be fired from the shoulder and designed to use the energy of the explosive in a fixed shotgun shell to fire through a smooth bore either a number of projectiles or a single projectile for each pull of the trigger.10 A shotgun subject to the NFA has a barrel or barrels of less than 18 inches in length.
2.1.2 Weapon made from a shotgun. A weapon made from a shotgun is a shotgun type weapon that has an overall length of less than 26 inches or a barrel or barrels of less than 18 inches in length.
Featuring a 14-inch barrel, “birds head” pistol grip and an overall length of 26.37 inches, the Mossberg 590 Shockwave (and Remington TAC-14) does not fall under the purview of the National Firearms Act (NFA) and does not require additional paperwork or the payment of a tax stamp for transfers.
The obvious technical design hurtles for the semi-auto depiction in such a small configuration with a birds beak have already been mentioned.
My Remington 870 with 7" barrel was born as a registrable NFA "any other weapon", AOW; not a shotgun. Add a shoulder stock and it is still an AOW, as it was never born a shotgun, thus can never be a "short barrel shotgun".