H. L. Mencken wrote:
“The Gettysburg speech was at once the shortest and the most famous oration in American history...the highest emotion reduced to a few poetical phrases. Lincoln himself never even remotely approached it. It is genuinely stupendous. But let us not forget that it is poetry, not logic; beauty, not sense. Think of the argument in it. Put it into the cold words of every day. The doctrine is simply this: that the Union soldiers who died at Gettysburg sacrificed their lives to the cause of self-determination—that government of the people, by the people, for the people, should not perish from the earth. It is difficult to imagine anything more untrue. The Union soldiers in the battle actually fought against self-determination; it was the Confederates who fought for the right of their people to govern themselves.”
Iirc Menken was, like Roger Taney, a Marylander, which may help explain why he so quickly dismisses the self-determination of four million slaves.
But more to your point, saying it was "all about" Southern self-determination is like claiming WWII was all about, say, Japanese self-determination.
Indeed, the Japanese threat to the U.S. homeland was orders of magnitude less than Confederates.
Consider this: "self-determination" also applied to Western Virginia, Eastern Tennessee, Northern Arkansas, Missouri, Kentucky, Oklahoma, New Mexico, Maryland, Pennsylvania and several other states which were, ahem, visited by Confederate armies.
The south was engaged in self-determinism when they turned their backs on their Constitution and countrymen. What they attempted was to force a unilateral (southern) determinism upon the entire continent.
Yes when looking for the underlying truth of a matter then who better to get it from than a newspaper satirist?