I would add to the discussion that since WW2 there has been a draw in Asia among the expeditionary powers with primarily a streak of independence among the weaker states including China and India which continue to this day. Roughly in chronological order:
- American occupation of Japan, preserving much of the local elite crushing political dissension and turning it into an ally.
- Civil war in China, resulting in the PRC on the mainland and the ROC on Taiwan.
- Civil war in Korea, US was the main force intervening on one side, China intervened on behalf of the other, resulting in the North and South.
- Independence and civil war in Vietnam, France then the US intervened on one side, China and the USSR intervened on behalf of the other, resulting in an officially Communist country which behaves very much independently.
- Many other peoples subject to colonialism were either granted or fought for independence, often a combination of both. All countries in Southeast and South Asia belong to the Non-Aligned Movement which was spearheaded by the most populous countries in the regions India and Indonesia together with Egypt, Ghana, and Yugoslavia.
- USSR intervention in Afghanistan which was defeated by locals supported by Pakistan, pro-Western Arab countries, the US, and China.
So I would say nobody had primacy over Asia, but certainly not for lack of contending by all sides, and much of this equilibrium persists to this day.
The real change now is that China's development has gotten to a point where it needs and wants to change the international setup which has been an extension of the colonial system, not unilaterally but by inspiring and leading others also disadvantaged by it, therefore by default at the expense of the current setup's beneficiaries - the US being the main one by far. The US for its part has so far chosen not to accommodate China or others, though it arrived at this juncture due to its own development in its own unique circumstances as the primary world power particularly since the end of the Cold War and after the curveballs of the 9/11 attacks and late-2000s financial crisis.