It includes such objects as could reasonably be used as weapons in the context of a well-functioning militia.
In all seriousness, arms included swords, pikes, knives, battle axes and hatchets, as well as firearms at the time the 2nd was written. I do not know if they meant to include crew served weapons (cannon), but the folks who could afford such were not likely to be other than responsible members of society, at least on land. Blasting powder (the premier explosive of the day)was not regulated, as it was only a different grind of the powder used in the firearms).
At sea, some unsavory types seized entire vessels with cannon, but that is another story, and they flew a different flag (skull and bones.)
While arms are certainly more sophisticated today, the basic thought prevails. A wise, honorable, and noble person will use arms in a wise fashion, even without laws. Criminals will not pay attention to any law.
If there were no criminals, no predators, the rest would not need arms to defend themselves, but that genie will not be put back in the bottle in the world as we know it.
Would I knowingly live next door to someone who had a mini-nuke? If they bought the optional shielding package, but remember, that here in North Dakota, "next door" is often a mile or two away...