I'm a father to three boys, a life-long gamer and I limit my kid's screen time. That's not just PC/console games, but includes time on the handheld/tablet, TV, YouTube and Internet. I love computer games and the idea that I believe gaming is unnatural or believe the kids should be playing with hoops and sticks is not my experience. It seems uncharacteristically lazy thinking by the OP.
Perhaps the smug parent is the one who has found success by not limiting their kid's screen time? Most parents are simply trying to do their best in the middle of a welter of governmental/medical advice and media scare stories.
I generally accept scientific papers that demonstrate that there is no strong evidence for a link between screen time and time spent engaging in physical activity (which is good to help avoid obesity and encourage good health) and so the medical recommendations in place in the US and Australia may not be appropriate for all geographical regions, but there are far more practical reasons for the limit.
During the school week, the kids have an hour in the morning and four hours in the afternoon. They need time to eat with the family, which will reduce this somewhat. Homework and chores are unpopular, but necessary - and so introducing the idea that these must be done before screen time seems reasonable. The guys have to share screens with the adults (we don't have the money/space for one each) and so they need to take turns with us and with each other. They also have music practice, sports and social clubs, and other activities to fit in. In short they need to plan how much time they can afford to spend on computer time without it impacting on everything else on their plate including developing other skills and spending time with other people.
I'm sure this will change as they grow older. At their current young ages, they need help to make good decisions about spending their time. As they go through secondary education, then we can give them more autonomy. We know that you have not developed your adult decision-making facilities until quite late. That's what stops me playing games 24x7.
I am surprised by Shamus' blanket and blunt dismissal of screen time discipline and the parents who engage in it. I limit my kid's screen time like I limit their access to sugary foods. A modicum of a wide variety of activities, to my mind, is better than a lot of a very narrow range of activities. I have met kids who were pushed into developing very narrow skills sets (maths prodigies, for example) and I found the lack of balance and roundness to their experience very unsettling and strange.