Certainly an interesting list, never considered something like this could be legal...you do need to pick it up yourself or do they even ship it to you?
My friends abroad are always shocked by this. However, these sales are highly supervised. To buy a pistol online it goes like this:
First you must be 18 and have no felony convictions.
Then you pick out a gun you want from a website and pay.
The gun is NOT shipped to you. It must be shipped to an FFL holder (licensed gun dealer) in your state.
When it arrives at the FFL you have to go and fill out paperwork, then have a background check and in most states there is a waiting period. So you can't get it that day.
A few days later you can come and pick it up. If you are going to carry the gun you will have to submit fingerprints for a more extensive background check. Since I travel a lot with my gun, I additionally have a "Utah" permit that requires a super background check.
There are more background checks and expensive requirements if you want a silencer, short barreled rifle, sawed off shotgun, full-auto machine gun. It's more work and expense than many realize.