FYI --- that video is either a MOD or a BS edit for some wierdo. That doesn't happen in Fallout3; I can can assure you as I just finished the game a few weeks back and even made a second character.
The GARY GARY GARY you keep hearing is actually a totally other mission that happens way off in the storyline of the game. It looks like the author of the video spliced or added sounds from that peticular storyline ontop of the beginning of the game when you're born and meet your dad in the Vault. I can't explain it fully, I can just assure you the video is BS.
There is a trait you can get in the game that ACTUALLY helps you interact with children, it's called "Child at Heart." There are several quests where you have to interact, have conversations and get quests from children; so being more likable to them would open better dialogue and make your quests possibly easier. You can attack and hurt or children but as I recall you cannot kill children. I might be wrong but I think Betheseda did it so not only would it not screw your game up by killing a quest character.
I admit, I got mad at the game once, saved it and attacked some snotty kids in Fallout 3 to see what would happen. They don't die, even with rockets, they just run away and cry. No big deal, I just reloaded my game from the save point and moved on.