To further [muddy|clarify] the waters, it's not terribly difficult to petition the ATF to declare a firearm a curio or relic or to have it removed from the NFA. In particular, if you look through the C&R book, you'll see a number of examples of specific Winchester rifles, identified with serial numbers, that were manufactured with short barrels. Normally, they'd be an SBR, regulated by the NFA. All it takes is a request, accompanied by a letter from, say, the curator of a museum attesting to the value of the item as a curio or relic and the ATF can exempt it from the NFA and put it on the C&R list. That's not to say they will, but it's not too tough to ask.
But, as EOD Guy posted, the gun in the OP probably fits the exemption already allowed.
Well we don't rent pigs and I figure it's better to say it right out front because a man that does like to rent pigs is... he's hard to stop - Gus McCrae