Dear prasanth1, greetings!
I didn't watch the video, but is there democracy in India now?
To be technically correct what we have is indeed not democracy. The system can be called "constitutional republic", where the citizens as a group is sovereign, the nation fashions its life according to the laws passed in accordance with the constitution of the land, by representatives of the citizens, and minority rights are guaranteed. When people use the term "democracy" this is what is usually meant, not the absolute rule of the majority the term itself suggests.
Further, I think there is a major fallacy in your argument that a democratic form of government can work only if the population is some what homogeneous in their goals and wants. There are two obvious corollaries to this premise, namely, (i) a better form of government for united India is some sort of dictatorship, or (ii) for democracy to work, India must be broken up into homogeneous nation states.
(i) I submit to you, only a democratic form of government can work in a non-homogeneous country like India. A non-representative dictatorial form of government will alienate sufficiently large section of the population and will make the country even more non-governable than a democratic form. Otherwise, there will be constant strife which can be quelled only by brutal suppression. I hope you are not suggesting that would be better than the chaotic nature of democratic process.
(ii) Breaking India down to states that are predominantly homogeneous is an impossible task. Each state consists of many religions, castes, and even language groups. For example, Bangalore has a large Tamil minority. In Tamil Nadu we have large Telugu minority and so on. So, even if we break India down to smaller units, we will still have not enough homogeneity that you propose as a prerequisite for democracy to work.
Churchill is supposed to have said, "Democracy is the worst form of government except for all those others that have been tried." Whenever I think of Churchill an intense sense of aversion rises in me, but in this case, he is right.
Cheers!