Why do people even play chess? Why do some of the world's best intellectuals spend their whole lives just on a wooden board, rather than working on the betterment of society ?
Where am I wrong?


None of "the world's best intellectuals" spend much time playing chess. The only strong (GM strength) chess player who qualifies as an intellectual is Dr John Nunn GM who graduated with a first in mathematics from Oxford University at the age of 18. 


  Why do people even play chess?


The best answer to this was given by Siegbert Tarrasch who famously said:


  Chess, like love, like music, has the power to make men happy