As you are probably aware, military museums in Japan can be roughly divided into two categories: 'war' museums and 'peace' museums. 'War' museums are extremely controversial both in Japan and overseas, as they attempt to downplay Japanese aggression and colonial enterprises in the 20th century. Yushukan Museum is the most prominent of these 'war' museums, especially due to its association with the Yasukuni Shrine.

So yes, the museum is playing coy when referring to "The China Incident." "The China Incident" was a term used by the wartime government of Japan in referring to the Second Sino-Japanese War, as Japan refused to officially acknowledge that a state of war existed between her and China. The long-held justification for Japanese intervention in China was to help the Guomindang eliminate the Chinese Communist Party, which was as absurd to the international community in the 1930s as it is to us now. Right-wing nationalists in Japan continue to use "The China Incident" to downplay events in 1937-1945, which the Yushukan is also guilty of.

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Sources:

Lee, Jooyoun. "Yasukuni and Hiroshima in Clash? War and Peace Museums in Contemporary Japan." Pacific Focus 33, no. 1 (2018): 5-33.

Morley, James William. The China Quagmire: Japan's Expansion on the Asian Continent, 1933-1941. New York: Columbia University Press, 1983.

"Incident" is the literal English translation of the term that was -- and is -- used in Japanese, "jiken" (事件); this was used in Japanese for all kinds of violent and (less often) non violent politcal clashes. In other contexts it can be translated as "case", "affair" or "event", but in this context, "incident" is by far the most common. Translations are never more than approximations, particularly in historically and nationalistically loaded contexts, but there's a benign reading of this possible.

To English ears, "incident" sounds minimizing next to "war", but this is not necessarily "being coy"; any more than than an Anglophone is being coy when they use "9/11" to encapsulate all sorts of things ("post 9/11 military deaths", for example). In English, we used to use the word "Affair" in a similar way -- "The Agadir Affair" or "Panther Crisis". To some extent, the Japanese were reflecting contemporary European diplomatic usage -- where "Incident and "Affair" were commonly used for confrontations circa 1900.

The Japanese often use this term we translate as "incident" with dates, very much the way we say "9/11" -- compare with the "Ni Ni Roku Jiken" ( 二・二六事件 ) or "2/26 incident" (occurs February 26, 1936, an attempt by young officers to overthrow the government).

So in referring to the July 7, 1937 battle which starts WW II in China, it's commonly known as the Marco Polo Bridge Incident, or "Double 7 Incident"; you often see that used as an endpoint for a period; which would thus be 1895 to July 1937. That use wouldn't be unlike an American describing "the Roosevelt Administration from the first inauguration to Pearl Harbor". Specifics get generalized to refer to the larger conflict, so in Japanese "the Manchurian Incident" can be just a specific act of false flag sabotage in 1931, or it can be the entire Manchurian occupation.

The Japanese use of the term incident for what we might describe as "clash" goes far back in Japanese political history -- you can find "the Purple Robe Incident" in 1627, a battle between the Shogun and the Emperor over the bestowing of religious authority. You can find it used in 1808 to describe the entry of the British frigate Phaeton into Nagasaki harbor . . . that's "the Phaeton Incident", there's the "Blood Oath Corps Incident", etc.

Anyone studying Sino-Japanese history will find themselves knee deep in a blizzard of "incidents" -- the Manchurian Incident, the Mukden Incident, the Marco Polo Bridge Incident, and so on. Generally, the Chinese use the equivalent term in Chinese, the characters 事变 (Shìbiàn)

In English, it can sound purposefully opaque, and you'll find the Chinese recoil at the "Nanjing Incident" -- this is one of their complaints about Japanese textbooks . . . but to determine whether the term is a circumlocution or standard requires a lot of specifics about the context in which its being used.

See, for example

WILSON, NOELL. “Tokugawa Defense Redux: Organizational Failure in the ‘Phaeton’ Incident of 1808.” The Journal of Japanese Studies, vol. 36, no. 1, 2010, pp. 1–32.

Large, Stephen S. “Nationalist Extremism in Early Shōwa Japan: Inoue Nisshō and the 'Blood-Pledge Corps Incident', 1932.” Modern Asian Studies, vol. 35, no. 3, 2001, pp. 533–564.

illiams, Duncan. “The Purple Robe Incident and the Formation of the Early Modern Sōtō Zen Institution.” Japanese Journal of Religious Studies, vol. 36, no. 1, 2009, pp. 27–43.

Ferrell, Robert H. “The Mukden Incident: September 18-19, 1931.” The Journal of Modern History, vol. 27, no. 1, 1955, pp. 66–72.