"Sport is all forms of physical activity which, through casual or organised participation, aim to use, maintain or improve physical fitness and provide entertainment to participants. Sport may be competitive, where a winner or winners can be identified by objective means, and may require a degree of skill, especially at higher levels. Hundreds of sports exist, including those for a single participant, through to those with hundreds of simultaneous participants, either in teams or competing as individuals. Some non-physical activities, such as board games and card games are sometimes referred to as sports,"
Why have Chess? if its not a sport?
You said it yourself... sport is a form of physical activity.
And starcraft is certainly not a physical activity.
Im sure its possible to start a club or something like that but I doubt any school with their current views on video games would support it the way you’re talking about.
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