That was talked about actually in the decision around page 50 to 54 (I think it was without looking it up again) when it was talking about the equipment required for milita.
I can't remember if they were citing previous rulings or making their own comments.
The basic impression I got was that small arms (rifles, pistols etc) that could be used by an individual were covered, but larger arms were not as those were to be provided by the actual military, BUT for militia use.
It follows that the weapons described in the Act were in "common use" at the time, particularly when one considers the widespread nature of militia duty. Included among these militia weapons were long guns (i.e., muskets and rifles) and pistols. Moreover, the Act distinguishes between the weapons citizens were required to furnish themselves and those that were to be supplied by the government. For instance, with respect to an artillery private (or "matross"), the Act provides that he should "furnish himself with all the equipments of a private in the infantry, until proper ordnance and field artillery is provided." The Act required militiamen to acquire weapons that were in common circulation and that individual men would be able to employ, such as muskets, rifles, pistols, sabres, hangers, etc., but not cumbersome, expensive, or rare equipment such as cannons.
I think you got it right. Not being a lawyer I can't make out some of the arcane writings of the judges, but they seem to believe that only the possession of personal type weapons like rifles and pistols is protected by the 2nd Amendment.