Finding the balance between studying and playing is very important for children and also to their parents. I'm not a parent yet but I did experience being a student. I was a part time tutor in my younger years so more or less I had witnessed my nephews and nieces agonized because of their parents (my cousins) forcing them to study way too long during the day. The debacle was quite interesting to watch though. Kids love playing because it was innate to us as human beings. We love competition and breaking records because it is fun. I'm not saying that studying isn't fun but doing the same thing for the whole day can be counter productive, especially for younger children. If they are doing it for week then it's worse. Playing or doing sports in between study sessions is recommended because it provides a good opportunity to condition and relax children's minds. Some proven benefits are faster thinking and better knowledge acquisition.
Is eSports for everyone?
Technology is advancing really fast and now we also have a digitized form of recreation or what we commonly referred to as eSports. But the real dilemma in choosing between eSports and traditional sports is often happening in the upper-lower class, middle class and above bracket of the society. The reason is children and parents in the lower brackets have very little time for recreation. Most of time is invested in earning money and studying. If there are any, chances are the kids will lean to free recreational opportunities which are the physical or traditional sports. Which for me is not really bad as an option.
Playing an eSport can be very different for most kids. It can be cheap if a child is only paying to play, you can even rent a PC or gaming console if there's no budget for buying your own. BUT things can get lucrative because of skins, arcanas and other premium items in a game. Let's take MOBA games like DOTA 2 and LOL, here in the Philippines you can rent a PC for as low as 0.3$/hour BUT with premiums the expenditure could balloon to hundreds to even thousand of dollars if you're shooting for the rarest items.
In the case above, I think that if parents are considering eSports as a form of recreation it depends on the money they can spare. A well off family can support their children being lucrative in a game but for many normal families just playing a game would be enough.
Is there any advantage in playing eSports?
eSports is more of a mind sport if I must say. One of the advantages it have is that the rules in eSports varies from time to time or from season to season compared to traditional sports in which you have these fixed rule sets. For sports like basketball and boxing, it will take many years of consultation and deliberation to change even the slightest bit of these rules. Adapting in a more dynamic rule set is also a skill that can be used even outside the game. Anticipating and adjusting in such changes can improved decision making skills and flexibility in reactions to first hand issues in real life. It helps a child to make sound judgments in such unforeseen situations.
Some other advantages I can think of are higher degree of freedom and better networking. Although I think it can be a double edged sword with the right guidance eSports can also help children to gain confidence by expressing themselves to a larger group of people. They can also have different network of friends and communities in which they can interact and assimilate. For parents, it is imperative to avoid toxic gaming environments and communities.
I think that one of the best and rarest advantage of playing eSports is that you can also make a career out of it. In my opinion there are 2 very important factors to consider. One is the child should be have exceptional skills ( top 0.01% of the game population) and the the other one is that parents should be very open minded. Society has a different view from people earning money in unorthodox methods and somewhat it is quite understandable. In the olden days of China, merchants were viewed as one of the lowest caste in the society because at that time people had strong prejudice in 'buying low, selling high' scheme to make money.
If I'm a parent I would also choose my child to thread the secure path. To be an engineer, a doctor or any respected job out there is what most parents dream of and that's why a parent should be very open minded if they support their child in choosing a different path. Anyway, just to take note pro players earn several times more than some professionals do, so it's not really bad if we're talking about the money. XD
Why not BOTH?
Personally, I think that eSports and traditional sports can work in tandem as recreational activities for children. It is also important for parents to consider what their children like and in what department they excel in. Academics, sports or even eSports proper guidance and balance should be always considered to achieve the best results. Communication between children and parents is a great key to achieve success in any chosen field.
Note: That's quite a clickbait sorry. I'm not implying that eSports is a fake sport rather I'm referring to 'real' sports as the traditional/physical sporting activities.