How important is hunting for human subsistence? It depends on the environment.

Hunter-gatherer diet is systematically related to environmental characteristics, especially the effectice temperature and primary plant production. There is no question that many tropical and subtropical hunter-gatherers rely primarly on plant food (with women bringinging home most of the food).

But the colder the environment, the more food is derived from hunting and fishing (and the more food is directly procured by men). I do not believe that Homo sapiens would have been so successfull in northern latitudes without hunting large animals. What else than big game provides enough food for a hunter and gatherer in a long and cold winter? In these regions hunting is not primarily a ritual or religious exercise but a matter of death and life.