The book does not really define "Bismarck's European order", unless implicitly, in which case I would understand it as a system in which Germany was prepared for all likely contingencies. There is the mention of Bismarck's determination always to be one of three among the five major powers, but that is touched on lightly. Kennan writes of Bismarck's preference for avoiding involvement in the Balkans, among those he spoke of as "sheep-stealers", and at the same time the necessity he felt for maintaining Austria-Hungary.
The heroes of the book are the professional diplomats, notably N.K. Giers, the Russian foreign minister, and Bismarck. Giers I had never read of before; he was of Swedish descent, the son of a border-town postmaster, with little to depend on but his own abilities, and the tsars' sometimes shaky support. Kennan speaks well of Bismarck's management. He does mention Bismarck's odd anxiety that the Catholic powers would unite against Germany: odd because the Italian government was on bad terms with the Vatican then and for years, the French governments were during much of the time bitterly anti-clerical, and Austria-Hungary was neither especially strong nor very stable. But Kennan quotes a prescient admonition of Bismarck's to Alexander III:
Never before, Bismarck concluded, had the great monarchies of Europe has greater interest in avoiding war. Someone, after all, had to lose a war; and peoples were now in the habit of holding their governments responsible for such reverses.The villains, or anyway those who are not helpful, tend to be the nationalists. The Russian editor Katkov exemplifies the tendency, sure that Russia's misfortunes in the Balkans are to be blamed on the Germans and Austrians. The French had their share of revanchists in the press and government. The Hungarians, though not looking for war, seemed to have had a skill at saying things that enraged the Russians. And the military establishments and their leaders had a weakness for war scares: in Germany Moltke and Waldersee, in France both Boulanger and his enemies, in Russia various members of the general staff.
Kennan spent many years of his Foreign Service career in Germany and Russia. In the early stages of World War II, before the U.S. entered the war, he was stationed in Berlin, where he knew Moltke's great-grandnephew Helmut von Moltke, and had extensive conversations with him; the state security apparatus would have been unhappy with the fact, let alone the content.