I played plenty of games over the years without ever feeling motivated to take up a gun and shoot up a local school, space station or nordic kingdom. So I'm fairly skeptical that video games can be said to cause mass shootings. Do they have an impact of some sort? Probably.
The difference is whether there's a relationship or a cause.
The media has defaulted to ridiculing the idea that there's a connection, but its own stories described the 'gamification' of mass shootings with each new killer trying to get a "high score". I wouldn't take alt-right memes at face value, but there's an obvious overlap between pop culture and attacks like these. That doesn't however mean that the pop culture is the cause or that the connection is especially meaningful.
The shooters themselves have made those connections. And it would be silly to treat a connection between simulated violence and real violence as completely trivial when the connections are being made by the shooters, and the culture of gaming seems to play a role.
And we've had a major rise in mass shootings in the same era when 3D shooters became popular. Changes in gun laws didn't do that.
On the other hand, past killers, including the Manson Family, referenced pop culture without it truly being a meaningful link. In a recent article, I noted that the Mason Family and the Weathermen both drew on pop music and claimed to find signals inside it. That didn't mean that there was anything wrong with Bob Dylan or the Beatles. It meant that there was something wrong with the killers themselves.
Pop culture taps into emotions. And it can be a two-way street. The culture becomes a source of meaning. And an outlet.
I suspect that without 3D shooters, we wouldn't have had the amount of mass shootings that we did, or the "high score" element in which killers strive to better each other. But murderous impulses are like a river. The culture is a channel. The crimes would likely have happened anyway, they just might have taken a different form.