People really need to check the meaning of self-confidence. Those who have it as a rule don't need to brag. Bragging when there's nothing to brag about falls under douchbaggery.
He's not bragging at all; he's only making a prediction about himself based on his own perceptions because he believes in himself and in his abilities. Self-confidence is thinking that you you have what it takes to accomplish whatever you set your mind to. That's exactly what I get from that quote.