It had nothing to do with Russian industrialization.
"Nothing" is a very strong word.
The entire war started through a breakdown in relations in a matter of days. Hell, what I linked to earlier clearly showed reluctance to go to war; it only escalated when shit hit the fan in regards to Russian mobilization despite saying otherwise, causing Germany to feel betrayed and too started to mobilize for war.
The
Willy-Nicky telegrams are entirely overstated as a fear of war. Claiming that Germany felt betrayed entirely ignores that Wilhelm completely ignored Nicholas' efforts to ensure independent arbitration at the Hague, and that German ambassadors operating on the lead from Berlin were busily sending ultimatums backed by threat of military force, as Nicholas calls Wilhelm out on in one of the telegrams quoted on your link. It was an attempt to keep Russia out of the war while Austria-Hungary gave their Serbian allies what-for. The problem was that Russia could not easily back down again; the Germans and Austrians perhaps hoped for a repeat of 1908 and the Bosnian Crisis, but Russia had learned its lesson from that; Russia's failure to support Serbia then had already destroyed one government, and worse, Austrian revelations about Russian maneuvering in the years leading up to that had humiliated Russia, leading to Russia's reinvigorated military programs, especially that of 1912. Indeed, this was one of the major fears on the Russian side, that their rearmament was not yet complete, and the major reason they pressured Serbia into accepting the Austrian ultimatum in the main, regardless of the cost of a repeat of 1908.
On a lower level than Wilhelm III, Russian industrialization did indeed have a significant militarizing effect on German politics; Moltke the Younger was the primary advocate of a preemptive strike against Russia in order to defeat it and prevent its industrialization and militarization programs from bearing fruit. Admiral von Müller described discussions to this effect years before the war, in fact, in 1912. Germany, from the highest level to the low, categorically refused to put any pressure on Austria-Hungary to lessen their claims or, when Serbia accepted the near-entirety of the ultimatum, to accept this acceptance.
Basically, when you say it started through a breakdown in relations in matter of days, you need to look at *why* relations were permitted to break down. Remember, this is not the first major crisis since the Triple Entente became entrenched against the Triple Alliance. The First and Second Moroccan Crisis, the Bosnian Crisis, and even the two Balkan Wars all failed to result in this major breakdown. The major differences between 1908 and 1914, however, are that Russia has begun a massive military and industrial modernization in 1912 with the aid of French capital, as well as the expansion of the French army. This threatened to overturn one of the fundamental assumptions of all German pre-war planning - the extended mobilization period Russia would require to put armies into the field, and undermined the requirement of German numerical superiority in the West as well. In other words, the German General Staff, as led by Moltke, became increasingly convinced of the necessity of a war to be waged in order to reverse these trends at the point of a bayonet.
EDIT:
I wouldn't put it past Germans to vastly overestimate the industrial growth potential of Russia, in order to justify high military budget to their elites, a la "bomber gap".
The devil of it is, they weren't overestimating it. At least, not by that much; their plans required Russia to remain a completely rural backwater without railroads or a modern military. Even an equalization of the military situation would have been enough to crush Germany between the twin vises of Russia and France.
Remember, Germany didn't even declare war on Russia; Germany joined Austria in its war against Serbia, who was allied with Russia.
And that is flat-out wrong. Germany did not wait for any nations to honor their alliances, except Britain - Austria declared war on Serbia, and three days later, Germany declared war on Russia. Two days later, Germany declared war on France. Austria doesn't declare war on Russia until August 6, three days after the German declaration of war on France. Indeed, if France had accepted the German ultimatum to remain neutral instead of giving an ambiguous response, the German ambassador was authorized and required to demand the cession of French border fortifications to ensure such.