My late grandfather used a slingshot to kill pigeons, squirrels, and rabbits. His was made out of a maple-wood laminate. He used hex nuts for the most part, but I've also seen him use creek pebbles. He always called it a "gum" sling. I guess they used gum to make the bands before rubber was widely available. He aimed it the same way the fellow in the video did. Once he drew the sling tight, he never moved from his cheek.
He could also kill almost anything with an old .22 single-shot Stevens. It had a hex barrel that was crooked, but he always killed the squirrels with a head shot. Around Thanksgiving he and the other men in the area would slaughter hogs. He was the one who could kill them with one shot to the head from that old .22 Stevens. He let me handle the .22 just once. I couldn't kill this old sow with five shots. That was the last time I helped.