I was going to go for something similar, but this is perfect. The real problem is not just Wilhelm, it is the impression in Germany among the power brokers that colonies and navies are the real deciding factor in international prestige. That attitude would have to change across Germany. The navy was also the place for the middle class to advance, whereas the army was still traditional and nobility focused in the higher ranks. Technologies were looked down on, as were the technical branches like the artillery.
If the Kaiser was strong enough morally to stand up to the German movement toward colonies and an enlarged navy, things would change drastically. Britain would not be nearly as threatened by Germany, but in colonial and economic disputes, Germany would not be or feel strong enough to take a hard line with countries like France. However, with extra money being channeled to the army, it could easily have two extra armies and the smaller armies of OTL like the 7th could have had several more corps. This would mean more active corps instead of reserve units, and probably more corps artillery for the reserves, which they lacked historically. Come 1914, if there is still a war, which I personally think there will be, as the economic elements will still be there and Britain will still be anti-German due to economic competition, though the average citizen would not be nearly as rabidly anti-German without the naval challenges and colonial disputes.
Germany would be much better off during the war, as they would then have more artillery and ammunition on hand at the start, as well as the ability to make more than historically, as all the extra guns would require extra manufacturing ability. Also, the heavy big bertha guns of the 420mm variety, which were still in production at the start of the war, would have more funding and would probably be available for immediate used instead of Germany having to borrow from Austria.
Now, as to the actual conduct of the war, it is hard if not impossible to add any extra troops to Belgium, as it logistics were stretched to the breaking point historically. The extra two armies are going to be headed east, which means that Conrad's plan to chop off Poland may very well go ahead and he won't be left to hang in the wind, getting demolished in Galicia while waiting for German support that never came. Poland falls early in 1914, while the Russians take the offensive against a much better prepared enemy. Austria is much better off and Conrad not seen as a fool as early when his early victories in Galicia pay off because the Germans are poised to support him. Also, the important two extra corps are not sent east during the marne, which means that the retreat to they Aisne line is not necessary (perhaps).
http://www.firstworldwar.com/maps/graphics/maps_03_easternfront1914.jpg
In the east the Russian 1st and 2nd armies attack into Prussia and fight the German 8th and 9th armies, which ends up likely not nearly as successfully as Tannenberg, but still in a German victory. The 10th army goes south before the Russian 9th army is ready, which means they breakthrough the fortress/river line of the Narew. This draws off the Russian 9th army and reinforcements from the Warsaw garrison, and likely the Guards from the Petrograd garrison, sparing the Austrians the collapse of their line in Galicia, at least around Lublin. They keep advancing on Syedlets while the Germans are forced to fight through to there.
The capture of Poland is offset for the Austrians by the loss in East Galicia, where they are forced to retreat. But the losses up north force the Russians to draw off troops to fight the Germans there, where they are outmatched. Eventually the arrival of the Russian 10th army in September and the reinforcements from Galicia allow the Russians to hold the Germans, but it also allows the Austrians to save Galicia and halt the Russians by flank attacks from the freed up 1st army and the newly arrived 2nd army. Still the Russians will be firmly entrenched in Galicia, though without making it much beyond Lemberg if even that far.
Overall things are much better for the Central Powers in 1914, though not war-winningly so. But it does set an important tone for future battles that means the Russians are in trouble. There is probably not much more of a change to the Western front, though there are most certainly more French losses. There are probably no major naval battles like Jutland, but more likely there is a greater focus on the Baltic sea and Russia.
By 1915 there is a much greater change, as the Austrians are not going to be ground to pieces in the Carpathians, but there will be some ugly battles with the Russians. Overall things are better without the loss of so much of Galicia and the fall of Przemysl and the need to transfer to much strength from the Serbian front to Galicia. The Germans probably focus more on the Western front in 1914, as during the Race to the Sea they can bring more strength to bear and won't need to switch any of the new reserve corps east. That mean 6 corps go west instead of 4, which tips the balance even more into Germany's hands during the campaign. Not enough to really affect a total win, but maybe enough to cause a breakthrough to the Somme.
Overall, the additional armies and troops in 1914 mean that Germany is much better prepared for war vis-a-vis their enemies, which then makes them more likely to win in the long run. It also gives them a larger pre-war professional army to maintain the quality of the armed forces during the expansion of divisions. It also means that when the triangular division is created, more corps result from the move, as there are more divisions to reduce in size. Many more professional, experienced troops=greater chance of winning for Germany and more allied casualties.
