Don't underestimate the role that the growing sense of nationalism that was sweeping across Europe at the time played in the Great War. I agree with all the facts above, but in many ways most of the countries in Europe were looking for a way to assert their dominance and prove that they were ready to stand as the leader of the continent.
The main actors at the war's outbreak were enmeshed in the two major alliance systems of the early twentieth century. The Triple Alliance consisted of Germany, Austria-Hungary, and Italy; and the Triple Entente was made up of Great Britain, France, and Russia. Many of the nations also had alliance obligations to smaller nations, as Russia did with Serbia and England did, more or less, with Belgium. When the war broke out, of course, Italy did not join Austria-Hungary and Germany, but the Ottoman Empire, the other major player in the war, did. By the end of the war, the United States and many other nations around the world had joined the Allied fight against Germany, Austria-Hungary, the Ottoman Empire and Bulgaria, who rounded out the so-called Central Powers.
WWI started with the ultimatum made by Austria-Hungary to Serbia in response to the assassination of Archduke Franz Ferdinand. It then spread because so many of the "main actors" were in alliances with one another. For example, Russia was allied with Serbia and France and England were allied with Russia. Germany was allied with Austria-Hungary. Those alliances truly got the war started in a major way.