What you have is a pistol grip only shotgun. Perfectly legal as a "normal" firearm. Cut down the barrel to less than 18 inches or an overall length of less than 26 inches and you end up with a "weapon made from a shotgun" which becomes an NFA item.
The pistol grip only shotgun must be transferred as a pistol, simply because it does not meet the definition of a shotgun which includes, "A shotgun is a firearm designed to be fired from the shoulder"
Also, more info:
Pages 2 and 3.
Actually, on the form 4473 it might be transferred as an "other firearm" instead of pistol... I am not sure which, but the requirements are exactly the same and both require the WA state pistol transfer form anyway. The ONLY thing that changes between Pistol and Other Firearm on the form 4473 is that one check mark in the box.