Arguably, the Napoleonic Wars are not the first “world war,” if we take that term to mean a conflict involving the great powers that was spread out across the entire globe. For example, the Seven Years War is sometimes presented as a candidate as the first “world war,” since it involved conflict in:
However, actually defining a “global conflict” or “world war” is a very difficult task. What constitutes global involvement is very debatable, especially when we bring conflicts of antiquity into account, since there was limited direct contact across wide geographic ranges. Wars prior to the Seven Years’ War also saw (albeit limited) involvement across continents, e.g. the War of the League of Augsburg and the War of the Spanish Succession. Obviously, later wars also took place on a global scale, as you have noted with the Napoleonic Wars. Ultimately, what constitutes a “world war” is a complex historiographical question; that being said, the Napoleonic Wars do not necessarily fit in with the multiple theaters on multiple continents that we see in other global conflicts (e.g. the Seven Years’ War and the two World Wars). Napoleon’s strategy remained focused on dominating Europe through military action and the Continental System. Two of France’s major colonies in the New World (Haiti and Louisiana) were lost at the beginning of the conflict and thus did not participate, while Britain took control over many other colonial possessions. While there were related conflicts at the time, e.g. the War of 1812, and the Latin American wars of independence, the association of these wars with the Napoleonic Wars is another historiographical question a little outside the scope of my experience. If they are treated as separate conflicts, then the Napoleonic wars are somewhat less global than other “world wars.”