The French and Indian Wars, which began in 1754, led to the Seven Years War beginning two years later in 1756; both ended in 1763. Why is this not considered World War 1? It was a world conflict, was it not? It changed the balance of power in the world (with Britain in the primacy), did it not?
Continuous war was not possible
That period of war, mid 18th century, was before the industrial age. The ability to supply an army continuously in the field did not exist until the time of the railroads. Note that even during the American Revolution, both armies went into "winter quarters" more than once during a seven year war. (1776-1783, though after Yorktown most fighting was over in 1781).
That is one reason that those who called the first world war World War I (after the fact, since it was frequently called "The Great War" until the next one came along in the late 1930's) gave it that name.1
In sheer magnitude, the scale and scope of The Great War (WW I) dwarfed such wars as the 7 Years War/French and Indian Wars. The speed at which different parts of the globe could be reached and influenced was markedly different when ships were powered by coal and oil. (A hint of this was demonstrated in 1905, Battle of Tsushima Straits, between the fleets of Imperial Japan and Imperial Russia). Global reach in less time.
Even the Napoleonic Wars (from Marengo to Waterloo) whose scope was the whole of Europe for almost 20 years, is not called a world war, even though the scope of those wars once the "levee en mass" began was well beyond that of the Seven Years War and other wars of the ancien regime. The Napoleonic Wars ran as far afield as Egypt, included the pseudo-war between the US and France in the late 1790's (XYZ affair), and can include the scrap between the US and Great Britain (we call it the War of 1812) as an included case. Even that era of warfare was practically constrained by the limitations of feeding and supplying armies for the campaigns.
Before the industrial revolution, this simply wasn't possible.
(Mostly from memory, from a theory of war class, US Army Staff College, mid 1990s).
A later paper addresses the core theoretical basis behind this answer (in terms of the industrial age opening an entirely new age of warfare):
According to Schneider operational art is a unique style of military art. Operational art, Schneider claims, became the planning, execution and sustainment of temporally and spatially distributed maneuvers and battles, all being viewed as an organic whole.
Without Operational Art the means to conduct a World War, as meant by those who coined the term, simply was not possible. Schneider has argued that the American Civil War was, thanks to the distant home lands being able to supply armies in the field by rail(for a continuous campaign season) and its length was arguably the first of the industrial age's wars.
I agree with him. It was longer than France-Austria(1859), Prussia Danish (1864), and Prussia/Austria (1866). The Franco-Prussian of 1870-1871 certainly followed a similar pattern of harnessing industrial age means to the ends of war, albeit the war wasn't as long as the Civil War.
1 The first world war was first called (by some) "The first world war" back in 1918, although it's not what most people called it. (According to the BBC and QI: http://qi.com/infocloud/the-first-world-war) ... Thanks to @Arthur for updating me on that. @VladimirF advises that "It was called World War in other languages as well right after the war if not already during it. "The Fateful Adventures of the Good Soldier Švejk During the World War" is a fateful translation."
It actually has been described as such:
The war has been described as the first "world war", although this label was also given to various earlier conflicts like the Eighty Years' War, the Thirty Years' War, the War of the Spanish Succession and the War of the Austrian Succession, and to later conflicts like the Napoleonic Wars. The term "Second Hundred Years' War" has been used in order to describe the almost continuous level of worldwide conflict between France and Great Britain during the entire 18th century, reminiscent of the Hundred Years' War of the 14th and 15th centuries.
As to why none of these went down in history as world war one, I believe Tom's and Korvin's answers sum it up:
- WW1 was different, in that it was the first with years-long continuous fighting.
- Until WW2, WW1 was called originally the Great War.
I can think of several reasons.
1) Temporal proximity to World War II. As Korvin pointed out, World War I was named (retroactively) with reference to the war that took place 20-30 years later. The Seven Years' War was over 200 years earlier, not associated in people's minds with World War II. If you take the argument that the Seven Years' War should have been "World War I," then World War I would have been "World War II" and World War II would have been "World War III."
2) Lesser geographical reach. The Seven Years' War involved Europe, North America, and India, about half the world. The "World Wars" involved these plus East Asia (the more populous part), Australia, Africa, and tangentially, South America (as suppliers of goods to North America and Europe, not as fighters).
3) The magnitude of the conflict. World War II cost 50-80 million lives, depending on the estimate. World War I cost about 20 million lives. The Seven Years' War, closer to 1 million, an order of magnitude lower. This is true, even adjusting for the differences in World population; 1750 population was about 1/3 of 1950 population.