score:7
They didn't trust Italians…
German Empire and Austria-Hungary were allies and agreed for mutual support in case of war. That means Germany may rush South to help, or Austria may rush North to do likewise. And by then railways were a must for all armies.
Looking at the map for the state-owned railways in 1912 shows
And specifically for the Royal Bavarian State Railways
Thus the popularly so called Karwendel, which is really the Mittenwaldbahn conveniently plugs right in the middle of a huge gap in connectivity that is extra difficult terrain because of all the mountains:
That was of utmost importance to protect against Italian ambitions. Remember that South-Tyrol, Slovenia etc were part of the Habsburg Empire and apart from Triest and Fiume the mainly Croatian coast Austria's access to the Adriatic.
The lowland connections along the Danube towards Salzburg are easier travel, but an enormous detour. While its true that Upper Austria was "the land of armament factories" (Steyr, Mannlicher etc.) and other main centers were Vienna, Prague and foremost Pilsen (Skoda), the actual manufacturing of any weapons and supply is only half the story. Deployment and moving around of existing weapons and supply is the other half…
From the Austrian side:
— Isochrone Map: Austro-Hungarian Empire Railway Network 1912 in English, 18. May 2015
And for the mentioned cannons:
— Marianne Enigl: "100 Jahre Erster Weltkrieg: Die gigantische Rüstungsmaschinerie der Habsburger", profil, 30. 7. 2014.
Those kind of guns aren't suited for being horse drawn.
The Austrian terminal of that railway is Innsbruck. The economical center for Western Austria. And since Emperor Maximilian's times an armaments center, of which until today 5 companies survive. The most famous probably Peterlongo, producing repeating guns "With strongest effect on thick-skinned animals." That company, Ganahl and Jester were a major supplier for the k.u.k army, producing revolvers.
This edge of the empire is also the hinterland for the Werk Valmorbia a fortified frontier facing the Italians. Innsbruck being the center for general staff XIV. Army Corps,
having numerous barracks and additionally a Landwehr Defence Command and first Kaiserjäger regiment.
One of the cannons alluded to in the book may have been the Skoda 305 mm Model 1911:
Eight Mörsers were loaned to the German Army and they were first fired in action on the Western Front at the start of World War I. They were used in concert with the Krupp 42 cm howitzer ("Big Bertha") to destroy the rings of Belgian fortresses around Liege (Battle of Liège), Namur (Fortified Position of Namur) and Antwerp (Forts Koningshooikt, Kessel and Broechem).
These weapons were borrowed together with two half-battalions (Krakau & Görz-Wippach), who both fought a well before Austria declared war on Belgium.
More on these types of heavy guns here, here, here and here. A short description of their use and admitting explicitly to use Austrian guns at Namur is the German account of the first weeks of the war in Der Weltkrieg 1914 bis 1918, Die Grenzschlachten im Westen (1. 1925), (p218).
Note that the Wikipedia quote seems incorrect in associating the Austrian guns with Liege. It seems that only at Namur they really saw action (Cf. Clayton Donnell: "Breaking the Fortress Line, 1914", Pen and Sword Military, 2013. (p43))
And if you look at the map for the battalion from Görz-Wippach, you'll find that town Wippach in Slovenia now and Görz in Italy. Meaning the shortest possible route to Belgium was via the new railway…