To me they're asking the defendant, "What does your possession of this weapon have to do with the preservation or efficiency of a well regulated militia?" (ie., First, what does this weapon have to do with a militia? Second, what does your possession of it have to do with a militia?)
Even if the defendants could have demonstrated that shotguns (<18") were militia type weapons, I think they still would have had to prove that their possession had something to do with a militia.
Ask yourself, why was the USSC so interested in the weapons relationship to a militia? If the second amendment protects an individual RKBA, who cares about a militia? Why ask if this weapon is a militia-type weapon?
Because they wished to find a way to infringe a persons right to keep and bear arms. They have succeeded.
But, from US vs Miller we find:
The signification attributed to the term Militia appears from the debates in the Convention, the history and legislation of Colonies and States, and the writings of approved commentators. These show plainly enough that the Militia comprised all males physically capable of acting in concert for the common defense.
The Supreme Court in Miller was not silent regarding militia membership. It was not an issue in the remand and was not likely to be an issue at trial.
Also, note that they do not refer to organized state militias. They are referring to the unorganized militia, as were the Founders who wrote the Constitution.