So simply put a sport is an "athletic" activity generally done out doors. That requires some sort of physical ability.
Moving your fingers does not fall in this category. A good example to compare to is Chess call the "Gentleman's Sport" because it's not physically demanding, but demands a lot from your mind. League is no where near the strategic/intelligence level required to be a master of it, but it does require mechanics, reaction time, and cooperation.
Mixing the two you get an E-sport "Electronic sport" because it is a small mixture of both. You are more working your mind than your body, but you are still cooperating and testing skill.
Taking it to a basic level, nothing existed prior to video games similar to them, therefore a new term needed to be created. Esport just makes the most sense.
As far as change goes, Riot updates league to keep it as fresh as they can. To their detriment IMO they do not want to actually balance the game. Bringing in and out champions as they please. Balance changes "suck" because Riot has no intention to make them "good" (in whoevers opinion). It's not change for the sake of change though, they have the agenda they want to fulfill, they have their goals.
Personally I think that if Riot wanted to. League could be near perfect balance in months. It's clear who's weak and who's strong. Who's simple and whos not. What can be removed to make it easier, like unneeded ratios, and what can be added.
These changes though keep league feeling fresh if only artificially, but it's been working. I don't know what would happen if league was stabilized in a healthy state. I don't think Riot want's to find out though.
A game like chess is in a near perfect balance state the only advantage is who goes first since they start with Tempo. A White player can win every single game 100% of the time if they know every counter move to black. No one does, so this one flaw is not exploitable. The levers that are always changing then are the skill of players only making it so that the is changing and metas change, but not due to the dead developers lol.
In the NFL the health and skill is all that changes the game. While yes rules against certain tackles and safety rules exist, these normally don't have much impact on the game itself. The game only has a few basic limiting factors like active members etc.
IT would be interesting to see if Riot focus on balancing the game entirely and left it alone if it what would happen, but video games and esports tend to have bad track records when that happens. Even games like SC2 and AoE cannot stand the test of time League would probably be no different. Smash bros is a bit of an exception, but it's highly skill dependent. And it still is not near the level of League.
Sorry long explanation, just interested me was all.