What if humans had evolved to be the predators of a different species

Imagine that humans evolved to be the natural predator of a species, let's call it "glimmerwings". We would have evolved to hunt these creatures over hundreds of thousands of years and they would have evolved to avoid us. As a result, we would have developed traits that make us better suited to this purpose, such as enhanced eyesight, powerful legs, sharp claws and a strong bite. In contrast, other species, such as dogs or lions, would not have evolved in the same way because they don't have the same evolutionary pressures to hunt these creatures. What kind of implications would this have for our society, economy and way of life?