I'm still playing through the series to try and understand how this series somehow became one of the biggest in all of entertainment that this is even possible. I mean, yeah it's a great series. But to this level of mainstream success, to the point it casts a shadow over not just gaming, but almost all of entertainment?
I want to say because it came out at the right time within the right circumstances.
@Would is correct. Consider the video game landscape within the 90s, games were catering to more mature audiences thanks to shifting consumer wants. Think going from the Golden Age of Hollywood from noir, bloodless movies like
Mildred Pierce,
Double Indemnity and
The Big Sleep from the 40s to gangster geared, violent films like
Scarface,
Training Day and
Pulp Fiction in the 90s.
GTA during its 2D inceptions was a surprise success thanks to its unadulterated freedom to cause mayhem and freely explore a sandbox from its iconic gameplay mechanic of commandeering any car at will. Now, take that concept into 3D with the PlayStation 2's radically innovative technology and fan base, you have a recipe for success to live out a criminal fantasy like those gangster films.
There have been games that predate GTA III with open worlds, driving mechanics, in-depth stories, even violence, but GTA III was able to coalesce those aspects (and then some) into a cohesive, innovation product with its sequels refining that formula even further.
TLDR: the GTA series was unlike anything that has happened with video games thanks to its unapologetic violent material and innovative gameplay that allowed players to roam freely within its sandbox parameters.