I would assume it wouldn't be a 'world war' unless nations from all over the globe are actively engaged against each other with sides clearly defined.
Can't say WW2 started with germany invading poland simply because there was a war in europe and a war in china/japan when china wasnt an ally of allied forces of europe nor japan an enemy of allied forces europe at the time. It was european conflict not global.
You could say it became a world war when japan allied itself with germany, declared war on the US (by proxy making the US and germany enemies even if germany didnt declare war on the US until a few days later) and became enemy to allied forces including the british commonwealth... which made china an ally of the US and Britain practically instantly.
It was only until then that separate conflicts all over the world became polarized into allies and axis and the fighting became widespread on a global scale.
Using your logic then, WWII started in September 1940 when Japan formally became allies with Germany, linking the war in Europe with the War in Asia.
OR using your logic, a secret treaty between a European nation, lets say Germany, and a mostly Asian nation, oh how about we use Russia for the heck of it, to attack Poland in 1939.
Britain declared war, France declared war, there was fighting between German and British/French Naval ships all across the world from South America to the Indian Ocean.
