Of course. ESports are so much more inclusive than other depots. Even that crippled kid in a wheelchair can play a video game.
Let's look at it like this, chess is a sport. It's also a game. ESports are electronic games. If a game like chess can be a sport, a more intense game (such as most MOBA games or the commonly used FPS genre) should be classified as well. Both take the exact same things, strategy, practice, and the ability to do basic motions.
League of legends is a really cool game. So is counter strike. Success in esports doesn't depend on how athletic you are. Esports are real sports and schools support other sports. It isn't fair if they don't support esports. Increased interest in school functions and school spirit. Increased self esteem for nerds.
The purpose of a school is to teach. A school should not be a place to play video games, even as a job. Schools should focus on giving students the materials they need to study, not on giving wannabe pro gamers what they want.
Don't mistake me, I think that extracurricular activities are important to students but I don't feel as if the budget, both of time and money, should go towards outside activities.
If a school has everything they need then there is some merit to providing extracurriculars but it would be better for public schools to partner with sponsors in order to provide out-of school activities.
This includes real sports, under-funding math classes to the point where an ex-factory worker with an emergency degree is the standard teacher and funding p.E. To the point at which the three gym teachers complain about not having four. It's not a good order for priorities. Especially in a environment built for learning.