The OP is referring to WWII (since it alludes to Japan)
WWII was already a World War, even before t he US officially joined in formal declaration of hostilities against Japan, Germany and Italy. WWII had open conflict theaters in Africa, Australia, Asia (China, Manchuria, Parts of Siberia as well as India) and there was conflict zones within the zones of influence of certain powers in South America as well. The presence of the US is not what makes a war a world war, it is the scope of the war itself which encompasses multiple continents.
The United States entry and the subsequent use of its intact infrastructure and production capability to win the war for itself and its allies ended WWII but it was already a WWII before the US got in.