Perhaps he is using a section of the stone each time, depending on the angle desired? Regular stones are too small for such a long knife. It calls for some body rocking motion. I wouldn't doubt his professional skill as each fish would be too expensive for him to mutialiate... In all probability he has a way/ technique to use a dished stone..
I am not so sure the stone is concave... look at the edge he is flattening the ura and the stone seems to be pretty flat to me, I think it looks that way because of the shape it has, I think it has a corner sticking out, or the picture could be warped, look at the guy behind his face seems to be warped. I don't think these guys would risk maiming a several thousand dllr fish with a bad edge and by the size of that knife we are probably talking about the huge ton or more tunas which go for hefty amounts.