Causation is EXCATLY what correlation implies. It dose not PROVE causation. Correlation points the direction to look for possible causation.
Also note the original post does not claim to show causation, just correlation.
I have heard it said that correlation does not prove causation, but without correlation you cannot have causation. Here we have a case where there is not correlation, hence you can be sure that lack of gun control does not cause gun homicides.
If there had been correlation, then we would still not have proof, but cause and effect could have been possible. So the graph is quite meaningful. Is my logic incorrect?