^Look at my avatar - he meant it alright regardless of what he had up his sleeve, you could see the anger build in his face - who's benefit was that 'act' for?
Have you ever seen Kirk lose his temper like that? I mean, in TOS or something? By that sort of thing, Kirk was overreacting, and while Shatner may be an over-actor, this was way too much ham. No, I am sure that Kirk was pretending to be frustrated.
Tell me an example in TOS when Kirk was confronted by an antagonist who (Totally unjustified) personally held Kirk responsible for everything bad that had happened to him after their exile and made it his sole obsession in life to make Kirk pay for all of his misery. And was able to almost accomplish this goal killing a lot of people and causing massive destruction along the way. I can't think of one.
All of Kirk's enemies on the show were due to political or cultural issues or some person or alien race or machine just acting crazy. It wasn't a personal vendetta against him. Even when his brother dies it was just because of a creature acting on instinct, which happens all the time, not because some madman with a personal score to settle with Kirk had him killed in cold blood.
And this after Kirk in TOS had basically given Khan another shot at building a life in freedom when, for Khan's actions, he could have justifiably:
1. Blown away Khan with a phaser.
2. Returned them all to suspended animation in the Botany Bay and sent them into deep space.
3. Had them all thrown in the slammer and say to Khan "Good luck Khan....I hope your genetically engineered ass can protect you from Boggs and the Sisters (or the 23rd century equivalent)
Everything horrible that happened to Khan on Ceti Alpha V Kirk couldn't have possibly anticipated and was totally beyond his control. Khan was basically mad that Kirk didn't text him every few days to see how things were going, so when it all went to hell he could save them. It's not like Kirk beat McGivers to death with his bare hands in front of Khan or hung the crew of the Botany Bay with piano wire and made Khan watch.
Kirk thought he'd dealt with them much more humanely then they deserved, he'd given them a chance to have a life and now he had to move on with his own life and it wasn't his responsibility to check in frequently and ask "Everything going OK on there good buddy". Christ he even let Khan take one of his crewmembers because they loved each other when McGivers, out of all people, should have been tried for mutiny.
Speaking of McGivers Khan didn't seem to have a problem forgiving her when she sabotaged his plans to hijack the Enterprise, he even married her for God sakes. Granted she was a nice piece of tail and Khan wanted to tap that ass, but she had just as much, if not more for the Botany Bay crew being exiled. Yet he's obsessed with killing Kirk 15 years later when Kirk treated him better then he deserved and had absolutely nothing to do with the actual events that destroyed Khan's life.
That was the whole point of TWOK. Kirk had never experienced such a psychotic and determined foe who wanted revenge for completely personal reasons and as a result Kirk responded differently than he did to some Klingon or Romulan who hated Kirk because his government told him he was supposed to.
And if you think the scream was over the top I ask you, considering all the pain, death and destruction Khan had inflicted so far, all in the name of personal vengence, and was now openly taunting him, how was Kirk supposed to react? "Oh Khan you meanie head, stop this silliness now". The scream was great, it was acted great and it showed that even the mighty Captain Kirk had a breaking point which made him more human and relateable, especially at this stage in his life.
Nothing in TOS can even begin compare to the sheer personal level of hatred Khan had for Kirk and Kirk faced something he'd never had to before. Someone who was determined to hunt him down to the ends of the universe if necessary. That's what made the film a classic.