James Holmes correctly describes  the Monroe Doctrine, and distinguishes it from Chinese maritime claims:
Far from being a writ for American meddling, the Monroe Doctrine was popular in Latin America for decades following its inception. Why wouldn’t it be? It was a declaration that Europeans could keep their holdings in the New World but not expand them. It was a kind of ratchet. Once Latin American republics had wrested their independence from the great empires, it was permanent. Washington vowed to construe any effort to restore imperial control of American states – whether direct or by proxy – as an unfriendly act toward the United States. Few in Central or South America objected to a strong neighbor’s guaranteeing their independence against extraregional predators.
Quite right. I suspect one of the reasons that someone might liken current Chinese claims in the South China Sea and elsewhere with the Monroe Doctrine is that many Americans have a very warped and inaccurate understanding  of what  the  Monroe Doctrine  originally was . Because of Teddy Roosevelt’s later perversion of the doctrine, it is usually misconstrued as a license for American domination and interference in the affairs of America’s neighbors, but this was exactly the opposite of what Monroe proposed.
Holmes mentions President Cleveland’s involvement in the Venezuelan boundary dispute as the beginning of increased U.S. meddling in Latin America, which is partly right but also potentially misleading. Cleveland’s view of the boundary dispute was informed by his own anti-imperialist and anti-colonialist convictions. As Cleveland saw it, the disagreement over the location of the border between British Guyana and Venezuela was an opportunity for a European power to take advantage of a weaker republic. In theory, this was exactly the sort of dispute to which the original Monroe Doctrine applied. As it happened, the U.S. realized that the boundary dispute was’t such a clear-cut case of British perfidy, and then the boundary dispute was resolved through arbitration, which was actually what Cleveland had wanted from the beginning. The far more serious distortions of the Monroe Doctrine came later under Roosevelt.