Also known as Queen Anne's War. A World War involves far more than two main opponents going at it. Colonial America was one theater of a 7 year struggle that was fought mainly between France and England. It did not involve more nations. Though it was dispersed globally.
Where the Napoleonic Wars could very easily be considered the first modern World War. Being it was fought between several competing powers and over a far wider area of the globe.
There are some who would consider Alexander's conquests the first. Then otehrs who consider the 100 Years War a world war.