This shouldn't be seen as something to laugh at, in fact I've argued about the role some children should play in games and how they should have more serious roles in the Western sphere unlike the Eastern one where...I'm just gonna stop there before I go any further.
The point is we see children as the most purest creatures on the planet: young, happy, and so peacefully ignorant of the horrors of the world around them. Humans are the fifth Great Ape species and we're inherently social creatures as well as each of us having an internal sense of paternal or maternal instincts. If we ever see a kid getting picked on, whether we know them or not, or first instinct is stop it and come to the victim's aid. We see children as many things, all mostly pure and ignorant but when one succumbs to the many things they need to be ignorant to, s*** hits the fan. Someone making fun of your son is ground rules for an beat down but the killing of innocent children is the grounds for a full blown war of vengeance. The same way of how a kid being forced to fight his way out of a war zone might stir up some strong emotion, so should the fact that a child dying have just as much emotion.
I applaud Infinity Ward for being mature enough to actually address the horrors of what war would be like on the civilian populace instead of treating it like it was just for kicks or to kick the puppy. More developers should be willing to take chances like Infinity Ward did with MW 3 and I hope to see this as a sort of call to arms for more serious plot in games.
EDIT: Yeah I just watched it and it was nowhere near as dramatic as I thought it would be. It's just so....meh. I know I shouldn't say that but all there was during the whole bomb scene was there was a girl, then there was an explosion, then someone farted, and that was it. They could've made this a whole lot more dramatic but they didn't. I think Infinity is trying to recreate what made Modern Warfare 1 so special. It's like Infinity asked his friend what he thought of the story he wrote and his friend is like," Wow that nuke thing is great, you should do that more often," Infinity does but fails to capture the emotion of it, he just does it without thinking.