Your assertion that China was always ruled by one central authority is highly doubtful in itself and far from truth. Modern day China is not same as ancient Chinese kingdoms. Some Chinese kingdoms controlled most parts of China for some times in history as some Indian kingdoms like Mauryas or Mughals did. The timeline of central kingdom controlling large parts of China may have been more than that in India's case as India faced many more foreign invasions. Here's how Chinese empires fared through the centuries.
There was no idea of nation state or countries before 18th century either in case of India or in case of China. China became a country in 1949, before that it was Qin, Xia, Ming dynasties and these dynasties had no connecton to each other, similar to the case of India. British Raj did act as the catalyst for awakening nationalist feelings among the Indians but then that was how the winds were flowing in the rest of the World at that time with the rise of national states and idea of modern day nationalism.
IVC civilization bought by 'outsider aryans' is again wrong even if we go by the Aryan invasion theory according to which Aryans were the cause of its decline. IVC civilization extended from eastern India (Uttar Pradesh) to Afghanistan, with its trading port town in Gujarat. Indic culture has extended within the natural geographical frontiers of the Indian sub-continent and modern nation state of India encompasses most that geographically and is its cultural inheritor, since other remaining states of the sub-continent are anything but Indic now.