IF you define a World War as a war where troops from all (most?) continents fought on MORE than one continent the OTLs nomenclature is correct.
During the 7 years war Brits and French fought on other continents - even with and against native nations. BUT the difference to the later wars is that for example troops from teh Mughal empire did NOT fight in Europe or North Africa, the Indian allys of Britain and France did not leave the American theater. IF you define Australia and Oceania as ONE continent European troops did even fight in this continent (even if only a short time
)
In the Great war (WWI) you got European troops fighing in Europe, Asia Africa and if you count in Coronel and Falklands even in the Americas. At the same time you have troops from the Americas, Asia, Africa and Australia fighting in Europe and on other continents too. Independent states from ALL continents were involved in this war (Counting South Africa - not many other Independent states in Africa - maybe Egypt as semi Independent)
THE Napoleonic wars don't qualify IMHO opinion as the fights as troops from the other continents did not participate in European campaignes 8or campaigns outside their home continent - Russia and the OE are borderline. the War of 1815 was not really part of the Napoleonic wars, but more an Anglo American affair...
Another criteria is that in earlier wars the alliances were less formal. Only the European nations were in blocs while for example the Mughals or the Indian tribes were no formal part on the "coalitions".
But in reality ist only a matter of Definition... (US sailors pressed in UK sevice could make a case for american involvement in the Napoleonic wars and UK owned Australia
...