Basically, his thinking goes, the people of Haiti brought an earthquake (and all else bad in their land) upon themselves because they made a pact with the devil, to escape slavery to the French. He says, ever since those Haitians revolted against the French, the Devil has been at work... and voila, another disaster.
And he probably believes himself, and millions believe him...
My opinion, Haiti was made a slave nation by the Europeans, ruined, left a mess by the French, and has been punished by the Europeans, including we European Americans, ever since... like for Cuba, but worse.
Robertson - you are the antichrist.