The Mossberg 590 Shockwave is classified as a "Pistol Grip Firearm." That is how it should be entered into your A&D Record and recorded on the 4473.
It is neither a long-gun nor a handgun. Only long-guns can be sold to those under 21 years old so this firearm can not be sold to anyone under 21 years old.
An FFL newsletter article titled Recording Pistol Grip Firearms in the Acquisition and Disposition Record (March 2013 Volume 2 page 4) addresses the issue of recording pistol grip firearms in the acquisition and disposition record.
Another FFL newsletter article titled Pistol Grips and Shotguns (November 2009 page 2) states: “Other questions raised pertain to entries made in the licensee’s required records with respect to firearm “type.” These entries should indicate the firearm type as “pistol grip firearm”.”