The Cold War had battles in Korea and Vietnam and near escalations in Cuba and some that are only now coming to light.
Those were more like jostling for influence and prestige than real wars. If they were real wars Koreans and Vietnamese would fly the American flag today.
I think the moniker "World War" should apply when you have total war between all of the dominant powers on the planet.
If its only just comming to light it's not really a major event that affects every country in the world in a major way then is it?
Calling everything a World War diminishes the impact of those words.
And a few that haven't. Ever.