The ATF said it's not a firearm under the NFA but it is a firearm under the GCA. They didn't explicitly say anything about it whether it is or is not a shotgun, but the implication is that it is not considered a shotgun under either of those laws. That doesn't mean it's not a shotgun under Ohio law. What it is, unquestionably, is a shotgun barrel connected to a shotgun receiver, connected to a pistol grip.
Texas appears to be in a similar situation as Ohio. Here's part of a summary from Texas Law Shield:
The short answer here is that nobody knows for sure whether it's legal in Ohio. Just because you can legally buy it doesn't mean it's legal to own, because it's a complicated question and no Ohio authority has formally ruled on the question.In the absence of language in the Texas Penal Code similar to “intended to be fired from the shoulder,” can having a pistol grip instead of a shoulder stock automatically create a firearm that is not a shotgun?
When left without a clear definition, the jury would end up looking at the firearm and deciding whether or not it met the commonly understood definition of a shotgun, which is usually a smooth bore firearm used for firing small shot at a short range.
If in the eyes of the jury the Mossberg 590 Shockwave looked like a shotgun, then due to the 14-inch barrel it would be a short-barrel firearm and possession would be a third-degree felony offense under Texas Penal Code Section 46.05(a)(1). Therefore, we definitely advise caution when it comes to purchasing and possessing this firearm in Texas!