Semantics.
The whole concept of "states' rights" is an invention cooked up to preserve slavery.
So the 10A doesn't exist?
If it weren't, defenders of the Confederacy would be able to itemize these alleged offenses against "states' rights" - but they never can.
Then the entire Constitution is nothing but an exercise in semantics.
The notion that a state is an entity that has rights is a false notion with destructive consequences.
So the 10A doesn't exist?
Of course it does, but it says nothing about states having "rights."
Your posted link is full of rhetoric, but it boils down to: The federal government isn't doing enough to force free states to hunt down escaped slaves.
It specifically criticizes other state legislatures for not passing laws that South Carolina thinks are necessary.
The document essentially claims that South Carolina is leaving because the federal government refuses to interfere in the affairs of other states to impose South Carolina's interpretation of the Constitution on New York, New Jersey, Ohio etc.
So not only is the whole concept of "states' rights" an oxymoron as a constitutional concept, the South Carolina state legislature is engaging in ridiculously laughable hypocrisy by giving the federal government the following ultimatum: "Either use federal power to force Ohio and New Jersey to obey South Carolina, or we will secede."
"States' rights" indeed! What a joke.