It's really an extension of Kirk cheating on the Kobyashi Maru. He's made a career out of cheating and bluffing his way through situations (cf. "corbomite" et al) which is exactly what makes him such a dynamic starship commander.
He's definitely playing up the role of being enraged over the communicator, but in reality it's all for Khan's benefit. He's counting on feathering Khan's ego to make him think he has won so that a little further down the track he might still be able to take him by surprise. He knows that Khan can out-think him in a lot of ways, so he deliberately plays to his ego to try and get under Khan's defences. Psychological warfare.
Compare with Kirk's ploy when the Romulan Commander questions him and Spock in the TOS episode 'The Enterprise Incident'. He goes waaaay
over the top there too with his 'rage' at Spock 'betraying' him, but it's all part of a bluff on the Romulans. Same reaction, same ploy on Kirk's part.