Quoted: I have a real Scorpion, the thing that attaches to the back and folds over the top could hardly be considered a stock.  It is so short most people who use the gun fire it like a pistol.  This makes me question the ATF definition of a 'stock' - surely there must be some minimum dimension to qualify?

An OT answer to an OT question, but one which is worth keeping in mind:

BATFE does not have a definition of a "stock" per se, and thus there are no minimum dimensions. US law only sets such minimum dimensions for barrel length and overall length, and those only apply to long guns. There are zero dimensional restrictions on domestically manufactured handguns.

Instead, US law definitions divides Title firearms into two general categories: Long guns and handguns. (NFA firearms are in their own separate category, with some rules that do not apply.)

The definitions are fairly simple:
--Handguns are firearms that lend themselves to concealment and are designed to be fired while being held in one hand.
--Long guns are firearms designed to be fired from the shoulder. The law does not require that the stock be useful, comfortable or practical -- just that the firearm was designed to be fired that way.

The definition of a stock on a shoulder-fired gun has evolved over the years: It must be rigid (thus, a lanyard does not qualify, even when used in a tension rig to increase handgun accuracy) and it must be physically attached to the firearm (a separate buttstock that is held against a handgun by the shooter, with no actual attachment to the handgun, is not part of the gun itself and is legal).

Lawmakers in the UK -- and in Canada and other parts of the world -- have taken multiple approaches to regulating firearms that include banning or mandating specific technical aspects of guns on a national scale.

US laws on the federal level, OTOH, focus primarily on who can legally access firearms, and have left the "technical management" of firearms features to state governments. Rather than ban a design or type that is considered particularly dangerous, the feds instead move it into the NFA category to further restrict its ownership, or they ban its importation. So some state governments have passed their own "Assault Weapons" bans, and others allow rifles and shotguns but make it difficult or impossible to own a handgun, etc. This may be changing when the US Supreme Court issues its ruling in Heller vs. D.C. sometime next year.

Since the apparent intent of the Skorpion's designers was to theoretically use that spaghetti strap to allow the gun to be fired from the shoulder, it falls into the category of "long gun" regardless of whether said stock actually serves a purpose.