Anything in moderation. Running too much will kill you as assuredly as sitting too much. So will drinking too much water. Its just easier to do one of those things than the others.
Talking about "I want my kids to be fit" and "what is a sport" aren't even the same conversation, but trying to shoehorn it in is leading to confusion and apparently anger.
I've yet to see a half thought through argument about what makes a sport, nor obviously any consensus on what is or isn't, or what should or shouldn't. So what if we haven't yet, but don't fall back on anger and irrelevant political rhetoric to make your arguments for you.
Why Curling and not video games? Have you seen the curling athletes? Or professional Dart players? Bowling? Pool? What about professional shot-put throwers?
Not all sports are good for you, or provide you with adequate exercise, so why get so furious at considering another activity that requires far more skill?
Just be consistent. If your opinion is that only exercise makes a sport, there's nothing wrong with that. But don't be afraid to call out 'real sports' as 'not sports' - I imagine it'll create a whole lot less cognitive dissonance.
For me, if it doesn't involve a physical activity, a team, an object to pass around, and a way to score points, its not a sport. Way to many things are called sports for no reason - most 'sports' are largely just exercise, which imo isn't a sport at all, same with largely cerebral exercises like chess or video games...But heaven forbid anyone tells someone that their thing isn't a 'sport'! Them is fightin' words!!!
Since it is so, so difficult to take away the apparently vaunted title of 'sport' from whatever activity, its far more internally consistent to just say 'anything that people compete at' is a sport. Be it some of the most athletic mult-event sports like decathalons or gymnastics all-around, extreme exercise like super marathons, traditional team ball sports, or something less physically exhausting but more heavily centered on mental acuity like shooting competitions (bows, guns, darts) and esports.
Specifically regarding esports, 'sports' just like anything else might as easily be described using purely economic statements. Any successful enterprise generates revenue and customers, sports do with with viewers, ticket sales, and merchandising. The reality is that esports are massively popular, and getting more so by the day. We're not talking about the local interest that something like "American Football" generates, we're talking international viewership numbers in the hundreds of millions. At some point, I would think the simple greed of entities like the Olympics will justify including the likes of video games for their profit making potential, and to stay culturally relevant. Indeed, some colleges have been recruiting and giving scholarships to "eAthletes" for their "eSports" playing for this very reason (money, greed, cultural relevance).
Just like I'd not let my own children play a sport as ridiculously dangerous as football (nothing like encouraging your child to bludgeon their brains into mush before they get to college!), I'd probably not consider dozens of videogame hours/day as an allowable daily pastime. But who cares, that doesn't make either 'not a sport', its irrelevant to the conversation.