I think that when people think of India and sports, the most important thing that people think of is Cricket. It's the main sport that they play and harness in the country. They do not have a strong presence of any other sport in the country and it's a way for them to have fun.
I do believe Cricket should be named the National Game of India. They play it enough there, and when you think of Cricket you immediately associate it with India. Just like how baseball is associated with the United States of America, is the same thing with Cricket is in India.
Cricket should be named the National Game of India because of its popularity in said country. Much like baseball was named America's Pasttime due to its popularity in the country, cricket's the sport most people associate with India as far as their athletic environment is concerned. The game migrated from England to India, during a time where the former had imperial control over the latter. So India basically grew and evolve with cricket side by side.
While I have to assume cricket is pretty popular in India, I would have to assume soccer is too. I believe whichever is more popular should be names the national game of India. If its difficult to determine there's nothing saying that they both couldn't share the title for the time being.
Cricket should not be named the National Game of India. This is because it is not orginally an Indian sport. It would be fine for a country known for cultural integration like the United States, but India is still mostly Indian in ethnicity. They should have a game of their own held up as a national game.