Specifically, I am curious about what was being taught to students that would go on to become major players - as adults - in the events that led to World War 1.
It really would not have existed, at least not really until after WW2.
World History as a field is still pretty new-- as our courses in World History at most universities. Prior to that, the most common history class that any college educated individual would attend was Western Civilization (which still exists on plenty of campuses in the US). The ideal of the Western Civilization course was to tell a common history of Western Europe and its colonial progeny that took for a starting point Rome/Greece. This history was fairly novel at the end of the 19th century as it ran pretty counter to the nationalistic (or nation based) histories which had become vogue. Histories that for instance spoke to the antiquity of the French Nation or German Nation and celebrated its uniqueness or special position in Europe/the World. Western Civ courses stressed common ancestry and common destiny.
In this same vein we might track the emergence of New History led by James Harvey Robinson, who took the bedrock of Western Civ and built upon it a deeply progressive narrative of history that could explain how man (or western man) rose up from his primitive state to modern. This movement saw professional historians as antiquarians, whose work was too academic and remote from contemporary life. New History also known as Social Studies combines history, politics, geography and civics together. It's unlikely leaders would be familiar with this sort of history as Robinson really begins his project around 1913.
After World War One, there is a greater movement towards World History, though its still very much on the margins and seen as an amateurish thing to do by much of the academy. Leaders in this regard would be Spengler and Toynbee who formed new versions of world history out of a new civilization approach in order to range across space and time. Their attempt to create an all encompassing, cosmic-universality of mankind history was dismissed as imagination, philosophy, or rubbish. What Spengler in particular really wanted to do was explain why World War One happened-- and to him, the easy answer was that Europe had reached the precipice and was beginning its civilizational slide into oblivion.
Recognizable World History bubbles up perhaps most recognizably in the 1950s in the writing of Leften Stavrianos who believed that we should be taking “a view from the moon,” a higher unifying vision of the whole of human past. He argued that istorians should transcend the Eurocentrism of their discipline and the progressive narrative that ranges from Greece to Rome to Modernity and leaves societies like Egypt and China to the side as exhausted dead ends. The problem with Western Civ he believed was that it gave no global context to human history and left students with only a triumphalist narrative in which European Civilization comes to dominate the globe, which was certainly less of European Evolution while all other societies seemed static, frozen in time.
Allardyce, Gilbert. "The Rise and Fall of the Western Civilization Course." The American Historical Review 87, no. 3 (1982): 695-725.
Allardyce, Gilbert. "Toward World History: American Historians and the Coming of the World History Course." Journal of World History 1, no. 1 (1990): 23-76.