Consider the forces of each of the countries:
South Korea’s army is about as large as ours. Their air force and navy, while not at all comparable to our, are entirely capable of defeating North Korea’s air force and navy. South Korea needs us for strategic deterrence. To prevent China from attempting to bully it.
Japan has navy and air forces are the best in Aria, including China.
India’s army is larger than ours, albeit not with as modern equipment. It’s air force is much smaller and features mostly MIG-21s and Su-30s.
China’s army is twice as large as India’s. Its Air Force has the advantage of more modern aircraft (the J-10, China also has J-7 which is like the MIG-21). But, China would have to project force across Tibet. That is a long and tenuous supply line.
This is probably an uneducated question on my part, but are they after easier access to Africa and the Middle East without the complication of a ring of islands friendly to the U.S.? They would have to seize a chunk of land to make that happen.
China has been cuddling up to Bangladesh and other neighbors.
http://indiatoday.intoday.in/story/doklam-china-india-pakistan-bangladesh-sri-lanka/1/1024074.html
Not the Middle East and Africa so much as being able to project sea power.