Fine, then ATF Class 3 licenses, which are required to keep and bear some kinds of arms, are a breach of the 2A similar to how the 1A is being breached here.
NFL stuff is actually a pretty good example of largely pointless law considering that what it does is effectively just make the items in question more expensive by taxing them and artificially limiting supply. If you want to own a machine gun, a grenade launcher, or even a fully functional tank in US, you still can so long as you're rich enough to afford it (unless your state has laws banning it). There are no additional restrictions on who can and cannot own that stuff beyond the requirement to pay the tax.
2A: ... the right of the people to keep and bear Arms, shall not be infringed.
Congress making a law that prevents minors from accesing information is a clearly a breach of the first text.
Point of sale ID checks for guns are much less clearly "infringing on the right to keep arms". It is only limiting the sale, not the ownership.