Is league a real sport ?

it is a game of skill, and decision making not a physical sport along the lines of chess, and poker , billiards, darts , etc

Short answer: no. While many people will go on and on about how "oh, it's in our culture so it just has to be", let's not forget the age of this compared to other actual sports. While baseball/football/basketball/hockey have literally been around for more than a hundred years, the fact this game wouldn't even be out of elementary school if it was a kid sorta makes me think that it's too early to say that it is one yet. Give it time, and it could possibly become a "sport", but as it stands right now it's a game and could just as easily die off in the next 5-10 years.

There's a difference between a sport and an esport. What gets most people is that they cannot differentiate between the two. To answer your question, no. League is nothing like a sport or real sport especially if you try to equate it to basketball, football, soccer, etc. It is an esport however simply through the meaning of the term: competition facilitated through the means of electronic systems. League and several other games (popular or not) fall into this category.

There's not even a need or sources honestly. This is as easy as using a search engine for the question you have and developing your own conclusion.

There's a difference between sports & e-sports. And League is the latter.

No, but that doesn't make it any greater or worse because of it. It is an e-sport, not a sport, similar in some respects, but different in others.

It depends on what you mean by sport and why you are trying to define it. If you're defining it for some sort of personal enjoyment or as some sort of debate, then that's up to you and your opinion, nobody else. If you're defining it for legal reasons, such as for overseas work visas, then it definitely qualifies as a sport, by recent historical precedent.