Same reason that the Ed Miliband bacon sandwich photograph and a myriad of similar "manufactured gaffes" were a "big deal": they were funny! It's America's Funniest Home Videos: Politics Edition, except without Bob Saget (which makes it even better)!
It gets aired on the news. It's funny so the announcer makes a quick joke. Satirists pick up on it and make more jokes, as do some late night shows. Now it's suddenly a "thing" and it feeds back in the next day's news when someone says something "interesting" about it (such as "he was just hoarse"), and the feedback loop continues.
Why did the media and many pundits declare his utterance to be the end of his presidential campaign?
Because it sounds nice and expert-y? There is no real evidence for this claim. It was a speech after the Iowa primary where he ended third; this general pattern was continued for the rest of the primaries. Was it due to the scream and the attention it received? Who knows...