Perhaps the most important thing to note is that the Second Sino-Japanese War started well before either of the usual "given" start dates for World War II. The Marco Polo Bridge Incident that's usually held to mark the beginning of the Second Sino-Japanese War took place in July 1937, well before either the German invasion of Poland (September 1939) or the attack on Pearl Harbor (December 1941). Debatably, Japan had been at war in China from as early as 1931 when they occupied Manchuria, which had technically become part of a unified Republic of China in 1928 at the end of the Northern Expedition. To that extent, the Second-Sino Japanese War had been going on long before the rest of what we call "World War II", and while some would instead argue that World War II should be considered as starting in 1937 with the start of the Second Sino-Japanese War, if we use the conventional dates in either 1939 or 1941, then it clearly had been a war that had been on going for some time. Many of the largest battles of the Second Sino-Japanese War were also fought before the outbreak of war in Europe or between Japan and the United States. The Battle of Shanghai was fought in the latter half of 1937, the Battle of Wuhan in the summer of 1938. To that extent, I would argue it's inaccurate to say that it is the "Chinese theatre of World War II" as the conflict there would widely be considered to pre-date World War II. It would be accurate to say that the Second Sino-Japanese War ultimately became subsumed in the wider global conflict, as China gained allies that were also at war with Japan, but I would argue that the earlier start to the conflict means that it would be a bit improper to limit discussion of the Sino-Japanese War to simply being a "theatre" of World War II.