[Sasparilla]

“This too is a pistol.”
With the rear stock, isn’t it classified as a short barrel rifle?

[timlilje]

Carbine
If it is using “Pistol” ammo

[Jaxter]

"With the rear stock, isn’t it classified as a short barrel rifle?"

Nope. That's not a stock. That's a "stabilizer". It's designed (wink, wink) to stabilize the "pistol" so you can accurately fire it one handed. If it was designed to fire two handed it would be illegal. No kidding. They come with a letter from the BATF (or whatever they call it these days) stating that they are legal.

[Yo-Yo]

With the rear stock, isn’t it classified as a short barrel rifle?

That's not a stock, that's a Sig arm brace. There was yet another stink with the ATF last January when they decided that the Sig Arm Brace was legal to attach to a pistol, but if you tried to shoulder it you were "remanufacturing" the brace and creating an SBR.

"Proper" use of the Sig brace: