Well, there are non-violent games that are very popular, normally sports games. I don’t think anyone finds baseball or basketball particularly objectionable. That said, if you had a traditional “adventure” or “strategy” based game, I’m not sure how’d you scrub out all the violence.
A few random-ish thoughts on video games: First, one of the most popular genre of games right now is so called “open world” games. Rather than traditional “linear” games that give you a single straightforward task (i.e “run this way, jump over these obstacles, save the princess.”) open-world games simply plop you down in the midst of a super complex world and let you make your own decisions. They can be quite violent and adult, but that’s the player’s choice, not the game’s. In games like Fallout and Skyrim you can be a murdering thief or an altruistic hero. You can solve every problem you come across with violence or you can talk your way out. The game doesn’t force you to do anything.
Second, I think people need to remember that the era when video games were aimed solely at kids is long gone. Most video games are no longer simple, straightforward things designed for 10 year olds. The best games are incredibly rich from a narrative perspective. There’s a ton of good character development and high production value. My point being that I think a lot of people see a game with a lot of violence, assume it’s meant for kids, and get disgusted with the idea of ten year olds being exposed to that. There are a ton of games now that are squarely aimed at adults, so we need to judge them by that standard.