If you read the sentence carefully, it's hard to read it as referring to the U.S. Constitution. If it did, the sentence would say that the Constitution is the supreme law of the land, no matter what the Constitution says.
Good point, but we aren't only qualifying against only the (U.S.) Constitution, we are qualifying it against the Constitution, Treaties and Federal Law. Another way to look at it is that the Constitution is supreme in all cases, and the federal laws and treaties are also supreme, unless they conflict with the Constitution (still referring to the U.S. one here) or state laws. In this way, Constitution > State Laws (which would reasonably include State constitutions) > Federal Laws and Treaties.
Specified group of laws 1: This Constitution,
Specified group of laws 2: and the laws of the United States which shall be made in pursuance thereof;
Specified group of laws 3: and all treaties made, or which shall be made, under the authority of the United States,
Supremacy assertion: shall be the supreme law of the land; and the judges in every state shall be bound thereby,
Supremacy exception: anything in the Constitution or laws of any State to the contrary not withstanding.
This really is an interesting conundrum. But be it State or National constitution that the exception is referring to, I'm still baffling at how any federal law (ATF, DEA, INS, etc) can possibly be thought to trump State laws governing the same under this clause of the Constitution.