I am not too familiar with the Indian voyages and I am a person who believes realpolitik.
I am interpreting this but; China's claim is based on the tribute model of historical sinosphere; not the Westphalia model Europe adopted or the older Christendom / Caliphate / protectorate international relations model.
To be a tributary is to accept vassal status and to accept the Chinese emperor is supreme over their emperor/king/sultan/etc. The domain is "technically" chinese in this perspective; and China is not a country or a nation but it is actually a cultural state. Borders were a foreign concept, just like the roman empire, the "border" was only meant to be a barrier to the non-Chinese and Chinese can easily go in and out.
Thus, here is a thought, every country/nation/empire around the south china sea was a tributary of China; whatever claims that these country can make, china "could" make as well. Japan was an exception, due to a shogun slight of hand.
We all know how China view the unequal treaties and the century of shame (and a bit before). Vietnam was lost to the french after the black flag army was destroyed, Korea was lost to Japan after the Sino-japanese war, Philippines was lost to the Spanish, Malacca was lost to the Portuguese (which lead to the extermination of all Portuguese in Chinese territory); Okinawa was taken by the Japanese.
The thing is, countries/empires/nations come and go. All claimants except China and Japan had been conquered/replaced. The only nation/country that still stands is China and Japan. Some may argue that China was conquered by the Mongols (Yuan) and the Manchus (Qing). But we must remember that these entities had been in the Chinese systems for eons. Kublai Khan of the Yuan chose to adopt the Chinese system and be himself written the mongol empire into the Chinese chronology as one of the dynasties. Shunzhi emporer, or the first Qing emperor to completely take over China also adopted the Chinese system and written themselves into the Chinese chronology. As the Nubian conquest of Egypt, do we consider black pharaohs not Egyptian as as the Nubian's adopted the Egyptian system and culture?
Infact, emperors of both the Yuan and the Qing posthumously pardoned generals and other persons in their preceding dynasties who had fought against their ancestors and have been labeled as traitors who sold their respective dynasties to the Yuan and the Qing; by looking at their own records. And in this aspect, they have celebrated these men as loyal servents of china. - For show? maybe. The illustration thou is that power have been transferred from one tribe to another all of which belonged to the same nation/country/cultrual identity.
The issues that we have, or more specifically the west have about China is that, china had to adopt the nation-state model after the Westphalia model after the century of shame. Asking China to make a historical valid claim on territory based on the Westphalia system when the historical claim is set prior to it is like asking a mandarin speaker to speak greek. it is a square pin in a round hole.
For thought, had China not fallen during the century of shame, in real Westphalia terms, Thailand, Vietnam, Malaysia, Philippines, etc. would all have been annexed as Japan had done to Okinawa which was a Japanese tribute vassal. All of this is of course history, but I think that from this angle, we can see why China claims historical claim.
