All this does is acknowledge that the secessions were, for the most part, about slavery. This is not sufficient to establish that slavery was the cause of the war.
This is like saying the cause of the Vietnam War was that North Vietnam wanted to unite the north and the south under one communist system; while this is an accurate statement, it does nothing to address the US’s motivation for involvement.
I can’t speak to the individual state declarations or constitutions, but the Constitution of the Confederacy included specific references to slavery and Alexander Stephens’ Cornerstone Speech, describing the basis of the Confederacy, is an explicit defense and promotion of slavery. Anyone arguing that the Civil War was not about slavery, at this point, is willfully and dangerously ignorant