Jamin Warren gives a good history of violent video games with Arcades, Mortal Kombat, Doom, Postal 2 & Night Trap. He notes that our culture over time has become less violent but that it's not entirely obvious.
What do you think? Will we always have violent games? Does it matter?

When I saw this series come up as a recommended subscription in YouTube, my first reaction was "What the hell does PBS know about video games?" Watching this episode led me to subscribe.
Turns out that PBS (or at least those involved in Game/Show) know quite a bit and are willing to get gamers talking about the headier topics surrounding our favorite hobby/obsession. This episode helps provide some historical perspective for many people that may believe the issue began with GTA III.
To answer the question posed by the title: Yes. As long as humans continue to create games, they will reflect the culture around them and their own impulses. So these violent tendencies will wend their way into any competitive endeavor.