People do realize the reason Shatner's "Khan!" scream is remembered is because most people think it's funny. Seriously, how much mileage have comedians and sitcoms gotten out of it in the last thirty years?
Most people don't consider it some dramatic moment that rivals the best other movies have to offer. It's remembered because Shatner is a ham and the scream was right up his alley.
Yup, he just screams for no reason, script, plot or otherwise.
The entire sequence of events leading up to the scream is the most puzzling scene in the movie. Khan could've just beamed Kirk up to the Reliant. He finally has Kirk cornered, and killing him isn't important, any more?
It may have been unfortunate that at the moment of Kirk's death, Spock sparks reminders to the audience of one of the most hammy moments in any Trek movie. But at least this time it had context, meaning, and real emotion. In story, it worked.