I would say it is still a Euro-zone conflict until 1940 when Japan and the US increased their roles. "World" is such a broad term. I know the commonly accepted date is September 3 1939, but that is as arbitrary as anything else until multiple continents became involved - Africa, eastern eurasia, and the americas weren't involved until 1940.

Also, Germany didn't help Japan, at that point they were invested in Chinese assistance, which made for a very tenuous diplomatic stance.

It sounds like most of the people answering here are answering from a European perspective and aren't aware of the literature and scholarship on this issue in Asia. This is an issue that continues to be controversial in Asia. Some feel the war should date to September 19th, 1931 with the Japanese invasion of Manchuria. Others would date it to July 7, 1937, with the Sino-Japanese war. There's a very political nature to these different dates, with right wing historians preferring the December 8, 1941 date, which downplays the violence and illegitimacy of Japanese colonial activities that occurred before that time. The right wing justification for Japan invading many Asian nations in the 20th century was to free them from European colonization. Left wing perspective was that they just replaced one colonial regime with another. These arguments continue today, with no one taking seriously the Japanese colonial justifications, except the Japanese right wing. Likewise the very name used to refer to the events is under contention, with some wanting it to be World War 2, and others The Pacific War, to emphasize Japanese aggression.

The problem with this argument is people are trying to create some sort of external algorithm for what defines a 'World War' based partly on when they want to be able to date their particular pet theory as being the start.

I'm not sure that we'd ever be able to come to a consensus on that algorithm so its somewhat pointless arguing over it.

So, I'm happy with the current dates...

I would also like to point out that even within Europe the the '39 date is not universally excepted. The Památník Druhého Odboje in Prague (which roughly translates to Memorial of the Second Resistance) for instance shows the dates 1938-1945 as a reminder that for the Czechs, the war started before the invasion of Poland.

edit: This page has a picture of the statue with the dates visible.