Legality of selling an MP 40 in an antique Mall? (OH, USA)

I know this question relates to a weapon of the 20th century, so remove this post if I'm breaking too many rules.

Recently, I visited an antique mall in Ohio. There was a booth selling many "souvenirs" taken by somebody's relative from WWII Germany where they served. Flags, medals, helmets, knives, firearms, and more, including a Luger and other handguns.

Among these items was an MP 40 submachine gun. I was under the impression that being an automatic weapon, this would require miles of red tape to sell and own, and has no place in an over-the-counter FFL free environment like an antique mall. Am I somehow mistaken?

Not trying to buy it or get anyone in trouble, just genuinely curious (edited for typo).