This most likely happened some place overseas at a place where tourists can pay a nominal fee to shoot automatic weapons, RPGs, and throw grenades etc… Not really any many safety measures besides the person standing beside you to tell you what to do.
In the video, the kid appears to be spooked when the safety lever ( a.k.a. the spoon ) flys off which leads to all hell breaking loose. Thank god for the quick thinking of the man in the white.
The grenade is most likely a concussion grenade (and not a fragmentation grenade as shown in the picture above from LIFE magazine). Fragmentation grenades disperse shrapnel upon exploding (wiki link), so I doubt they would be laughing it off like in the video if one of those were used.