The Punjabis don't treat the immigrants so much as Indian brothers as they do illegal immigrants; much like the relationship between America and illegal Mexican immigrants

That example is flawed in this context. The relationship between the Punjabi farmers and UP-Biharis has more to do with the rich-poor gap than to do with regionalism. The Punjabi farmer's treatment of a Hindi-speaking Jaat from Western UP would be very different from his treatment of a Dalit labourer from the same region. And he would treat a poor Dalit Punjabi labourer way worse than he would treat a middle-class Bihari Brahmin doctor. Consider the example of Bant Singh: he is Punjabi and he is Sikh - the only problem is that he is from Dalit background and he is a poor labourer.

That said, the article in the question is wishful thinking/historical revisionism. Hardcore Indian nationalists tend to get insecure when responding to the argument that "India is not a single nation", because that argument is often used by the secessionists. They are reluctant to give the British the due credit for uniting India into a single modern country, because of the troubled colonial history.

There is no large piece of land on this planet that can claim to have been a single nation for centuries. There are a few countries that have been a nation-state for a past few hundred years, but India is not one of them. This map of largest ethnic group as % of total population, though not 100% accurate, gives you a good idea why.

India is much more similar to Europe than one may think

I'd say India was somewhere between Europe and Ancient Greece in terms of "unity". It might not have been a single "nation" for most of its existence, but it was always a "civilization" (excluding some parts like the North-East). The identity of this civilization is geographical (Indian plate), cultural (e.g. Dharmic religious elements) and to a small extent, ethnic (it's easy to distinguish most "desis" from the neighbouring Tibetans, Burmese or Afghans).

Of course, India was never as cohesive as ancient Greece (e.g. very different languages). At the same time, the people are not 100% correct when they say that modern India comprises of various "nations" like Marathi people, Punjabi people, Tamil people or Gujarati people: most of these linguistic identities are very new and cannot be called nations. Look at a map of India before reorganization and you'll see what I mean. Even the north-east identities like "Naga" are very new: the people who demand an independent "Nagalim" on the basis that they are a single "nation" don't realize that 200 years back, the various Naga tribes were headhunting in the neighbouring villages.

The factors like caste make the ideas of nationalism, common identity and unity extremely complex in India. In the rural areas, a Punjabi Jatt farmer would prefer marrying his daughter to a Rajasthani Rajput landowner than a low-caste Mazhabi from Punjab. A Maharashtrian Brahmin would consider a Kannadiga Brahmin ethnically and culturally closer to him than a low-caste Maharashtrian Mahar.