First of all, GAMES like DotA, LoL, Counterstrike, WoW and many others all utilize a mouse. The ability to utilize your hand-to-eye coordination is a physical feat, as it originates from your muscle memory, i.e agility and precision. You need quick physical input. A professional player obviously excels at all these as this is a necessity to do well.
Secondly, read this:
http://www.chess.com/article/view/is-chess-a-sport"Claiming chess “is just a game”, because it is rule based, and therefore unworthy of undue attention, is a tautology (self-explanatory) and explains nothing."
Games are games, yes, but competetive gaming at high levels is not just "gaming". The level of competition is so high that the amount of effort you have to invest into becoming a better player kinda makes the idea of playing a game for recreational purpose an entirely different thing.
Thirdly, learn to use your own brain instead of looking up words in dictionaries. It doesn't require much intelligence to argue with the help of dictionaries, a monkey could do that.
Also, words change meanings. Sport is a fairly old term.
