No, that law was to conscript men (in times of war) into the militia, where they would be required to bring their own equipment (hence a militia). That was justified under the power to "raise and support Armies," not the commerce clause. In fact, IIRC not a single law cited the commerce clause until well into the 19th century. This sort of argument that comes from the left is pretty much outright lying.
Seems to me that many laws do not cite any clause of the Constitution. This thread started with reference to "An Act for the Relief of Sick and Disabled Seamen". The act does not cite what clause of the Constitution it relies on but what else than the Commerce clause could it be?
