Your English sounds curiously quite excellent - better, in fact, than most teabaggers posting here.
Assuming this is actually a question asked out of genuine interest from a "student in China", my suggestion is that you forget about learning anything about Jean-Jacques Rosseau from the noted war criminal Henry Kissinger.
Any knowledge acquired about Rousseau should come from professional philosophers and historians of intellectual history. I do not think it matters what the purported buzzword "rule of administration in the new social order" means. I am not convinced Rousseau actually said it, and since he wrote in French, this English interpretation could mangle the actual original meaning. The only thing that matters is intent....not buzzwords.
All I know about Rousseau is what I learned from a class I recently took --- that he was a contrarian voice to the Enlightenment. He, almost uniquely among the great European thinkers, maintained that cultural progress and technological progress lead directly to moral decay. The system of laws and property rights established by the modern nation state were forms of coercion and inequality leading to unnatural relationships. Primitive man living in balance with nature was deemed by Rousseau to be morally superior. As a deist, he was an ardent defender of a natural religion and God against the prevailing atheism of the day. It is possible that 20th radicals, progressives, and socialists might have held out Rousseau as their intellectual birthright, but that is their opinion and assertion only. Rousseau is dead and gone, and cannot speak for himself. I highly doubt Rousseau or Karl Marx would have approved of Bolsheviks or Maoists coopting their names in the pursuit of totalitarianism and the establishment of coercive Leninism or Maoism. .