No, that’s when WW2 became a pan-European war. It became a world war when Japan attacked the British and Americans, thus combining the Anglo-German and Sino-Japanese wars into a single conflict.

It's arguable, WW2 is typically dated from the German invasion of Poland. By then, the war in Asia was already underway with the Japanese fighting in Asia. So with the British Empire, Germans and French and the Soviet Union also starting hostilities, much of the world was at war.

This is because the history of WW2 is usually told from a Eurocentric perspective. The Soviets weren’t fully involved until 1941 either, since that’s when Germany invaded them.

Calling it a single conflict is bit of hair splitting, japan had almost nothing to do with germany, especially after war started. Those were 2 separate conflicts happening at the same time.

Part of what combined the two conflicts, aside from Allied questions about resource allocations and priorities, was the supply lines of the British Empire. There was a continuous series of supply lines running all the way from England to Burma, through the Mediterranean and Suez Canal and down through South Asia. The Suez Canal (under threat from the Italians and Germans) was part of the exact same supply line as the Burma Road (under threat from the Japanese).

Does anyone seriously think that the Nazis would have stopped at Eastern Europe?

It's what Hitler was saying he wanted, Lebensraum for a new German empire by conquering the "inferior" people of Eastern Europe. Western Europe probably didn't expect to be invaded, and who knows what kind of alternative history would have taken place if Britain and France hadn't got involved. Perhaps the Nazi's would never have been satisfied unless they were at war somewhere, or perhaps they would have had their hands full in the east. Nato countries today probably assume that Russia invading Ukraine isn't a prelude for Russia attacking Nato countries.