Is World of Warcraft a eligibale game for kids

That honestly depends on what you define as eligible for kids.
while the Games ESRB rating is T, if a child is mature enough to handle the competitive nature of the players as well as conduct themselves in a mature manner, then I would say yes it is eligible for that child. If a child is prone to tantrums and other such behavior then I would say that they should not play World Of Warcraft as this sort of behavior makes playing unpleasant at best for those playing the game.