Udacha6,
A variation of chess is very much an Indian game that existed many thousands of years ago. Even if you assume chess was invented in India, I don't understand why you would expect only Indians to be good at it!
But, coming to your question about the absence of world chess champions from India ... I guess you have never heard of Grand Master Anand!
The caste system was supposed to have originated based on the occupation of the people (again.. thousands of years ago). Broad categories were the ruling class, scholars, priests, warriors, merchants etc. People who were at the bottom of this chart are the so called "untouchables" today. Priests, obviously, elevated themselves to the highest position. This somehow continued to the present day.
However, since independence, to discriminate against or even call someone an untouchable will land you in prison quite immediately. At the time of independence, reservation at various levels were made available for these disadvantaged people with the thought that it would be phased out slowly. But, successive generations of corrupt politicians kept the reservation around just for a favourable vote bank.
That said ... I don't understand your correlation between caste systems and a country being democratic!! The affirmative action that is found in US and probably other european countries is similar to the reservation that exists for various castes which are deemed disadvantaged. Caste system is also similar to racism which is quite prevalent in US and most european countries. In US, discrimination against the blacks (the skin colour I guess gets decided at birth too.. or even before that) continued well into the 1960s (almost 200 years after the creation of the "DEMOCRATIC" nation) and yet you don't question its status as the most vibrant democratic country in the world. Wonder why?!