The Dean scream can only be understood in context and HM's portrayal of it removes as much context as the media.
It was the final act of the rise and fall of Dean during the Iowa primary, and Dean's ascension was largely due to media attention, along with his newly-proven tactic of using the net to raise nationwide funds. Three weeks prior to the scream, Dean was being Kinged as the new savior. His approach called for getting rough with the other side and attacking vigorously which caught the attention of everyone. Unfortunately it also had the effect of completely turning off the Iowa electorate, and his unexpectedly poor result let most of the air out of the balloon. And only THEN, YEeeaaaaagh!
The Yeagh was the least of his concerns, and the reason it was overplayed was because it was somewhat representational of his fiery attack approach being overplayed and leading to his demise. And because it was LESS damning than the REAL story, which was that Dean had dramatically failed and that his campaign had been dealt a terrible blow.
Similarly, during the 1992 election, the media made a big deal of George Bush 41 being very surprised by the newfangled technology of a supermarket scanner.
The event didn't really happen as described. But the story took hold because it was such a strong analogy for what people felt about 41.