With its utter freedom to roam the world and wreak havoc, GTA III has deeply influenced both open-world games and crime games, two very popular genres. Grand Theft Auto III was among the first living, breathing open-world video games, and Rockstar Games took that opportunity to let players become the virtual criminal/murderer of their dreams.
Shooting innocent pedestrians in the face seemed a lot more gruesome than stomping goombas in Mario, or even blowing up pixelated cartoons in Metal Slug. Its 3D graphics looked so realistic at the time.
It's easy to imagine why the media was afraid of Grand Theft Auto III on its release.