Sometimes all its six barrels would go off at once, and then there was no safe place in all the region round about, but behind it.
He was talking about a multiple barreled gun. I'm not sure the one in the pic is a pepperbox since it has one barrel. It looks like it's double action - pull the trigger and it cocks then fires the round.
According to that article, it looks like the transitional revolvers were also prone to chainfires.