I was watching a person use a dog ball thrower and was reminded of the woomera, a lever like device our first nations peoples used to throw a spear long distance. I don't recall any other cultures using anything like it, even the javelins of ancient Greeks were hand launched.
I understand that bows, crossbows and even ballistae existed, but I feel they're more of a "stored energy" type technology.
The short answer is yes. Similar devices which are used to improve the range and stability of thrown spears and javelins have been used by other cultures for millennia. A well known example from the Americas would be the atlatl. And the ancient Greeks and Roman's actually did use leather straps called amentums which served a similar process.
These spear throwers have been used by humans since the Upper Paleolithic, sometimes made of wood, leather or bone. The earliest findings come from France and date between 21,000 and 17,000 years ago. Although it probably was invented prior to this and there is some implicating evidence they were invented much earlier. For example the Mungo Man finds in NSW displays symptoms of arthritis in his right elbow which is commonly referred to as "atlatl elbow". It's still very speculative however and Papuan people along with Australian Aboriginals provably started using woomera between 6000BC and 4000BC. The lack of finds from Sub-Saharan Africa leads to the theory that they were invented by some of the earliest homo-sapien migrations out of Africa and gave them a competitive edge hunting megafauna during the Ice Age.