As a POD you'd be better served by the German 2nd army swinging wide and coming right into the flank of the BEF at Mons, wiping it out and then mauling the French 5th army in the aftermath. That leaves the German 2nd army free to go after Paris and the French 6th army, while not leaving a gap for the Anglo-French to exploit because the BEF is gone and the French 5th is too weak to try anything on the flank. Paris would then have to defend itself with the 6th army, which was no match for the full German 2nd army. Paris in encircled in September and falls no later than November. No Miracle of the Marne and the other German forces drive the French army back everywhere else. France is pretty much wrecked in 1914 and the Russians after the mess in 1914 probably come to terms either by the end of the year or in 1915 after losing Poland. Britain is a non-entity in the war and scoops up German colonies but for Ost Afrika. The Ottomans come in and Russia is doomed if they don't drop out, while Britain cannot help with the French done for in 1914.
So in the wake of that the British effectively have to cut a deal to avoid Germany annexing Belgium. Which would mean German Mittelafrika and accepting a lot of damage to France, not least of which is some border modifications, the destruction for French forts, and an indemnity and perhaps giving up the Ivory Coast in addition to the French Congo. Belgian Congo is definitely German. Maybe Germany is willing to give up Southwest Africa for getting Mittelafrika. Belgium is allowed to go free, but cannot rebuild their forts. France is no longer a great power, but is a significant regional one. Russia too is probably hobbled and loses Poland and perhaps Lithuania to give East Prussia buffer zone. Definitely recompense for any lost German property in Russia.
Britain really has very little alternative. If they opt to continue the blockade they lack the ships to pull it off once France falls and Germany can pillage France for food while it picks Russia apart with the Austrians and Ottomans, while the Italians will pretty much have to join the war if they hope to get anything, but on the CP side. The German navy is so powerful in WW1 that Britain will face a horrible naval conflict it cannot win once France falls. So they will have to make peace with Russia if they want to avoid a lot of problems, because the US is NOT coming to help them.
I think you're pretty close to the mark here. Perhaps the best P.O.D. might be to have an army group commander appointed at the outset, someone who could block the withdrawal of the two corps to East Prussia and also keep the the 2nd Army swinging wide. Still a logistical nightmare, though. I think your
Marne without Moltke is a more likely scenario - but maybe we give the Germans a couple lucky breaks, and something like this could happen.
In August, the remnants of the BEF flee back behind the Somme, leaving Kitchener the difficult job of trying to reconstitute the force with little time. The loss of the BEF on the far left flank quickly makes defense of most of the Channel ports untenable, with only fire support from RN pre-dreadnoughts delaying the Germans. Meanwhile, the Russian invasion of East Prussia is still crushed at Tannenberg and Masurian Lakes
Fall of Togoland to Anglo-French forces
Fall of German Samoa to New Zealand forces
Maclear repulsed in First Battle of Garua on 31 August, Kamerun
Goeben and Breslau successfully flee to Constantinople, resulting in the secret Ottoman–German Alliance
In September, the Germans reach the outskirts of Paris, and the siege begins. The French government flees to Bordeaux, and Verdun falls under siege. Faced with the the collapse of the Channel Ports and shocked by the virtual annihilation of the BEF, Territorials are called up and deployed to the southeastern coast. Asquith urgently calls for more reinforcements from India and the Dominions. The KM is emboldened to stage larger torpedo boat and submarine raids into the Channel.
Russians win the Battle of Galicia
Japan seizes the Mariana, Caroline, and Marshall Islands with virtually no resistance.
Serbs blunt Austrian advance at Battle of Drina
October: Siege of Paris turns into meatgrinder, as the French and British stake all on the outcome. Boulogne falls. Britain, under heavy pressure from Poincare to reconstitute a force for the western front, lands IV Corps at Dieppe, moving to a deployment behind the Somme.
The Maritiz Rebellion erupts in South Africa, and encouraged by the British catastrophe at Mons and focus on the Western Front, gathers strength quickly
Japanese land on Shandung peninsula
...
Well, the butterflies gather strength quickly at this point. The Turks are even more encouraged to enter the war at this point; conversely, Japan is even more keen to gobble up what German possessions it can while the war is underway. Italy, on the other hand, is rapidly getting a severe case of cold feet.
Assuming that Paris does fall in November, the French are in a pretty grim spot. They've lost the majority of their industrial base and their main rail hub, and the moral shock of losing Paris is a heavy blow. But it is hard to believe that the French would not fight on, just as they did in 1870 - they have allies this time, at least, and still have a well equipped army over over two million men in the field. Viviani's government would fall with Paris, however, and the entire PRS government is in danger of being discredited; the party in desperation probably turns to Clemenceau at this point rather than Briand. Clemenceau is a fighter.
At this point, the war would drag into 1915, but the Allied position in the West would only worsen. So long as the French fight on, Britain would feel urged to do so as well, albeit probably under a coalition government by this point. The French position finally collapses by late spring, and what remained of the BEF would be forced to fall back on Le Havre or Cherbourg for extraction. Faced with the Maritz Rebellion and growing unrest in Ireland, Britain would not be in a much better position. Clemenceau is likely forced out, fighting to the end, and a provisional government grudgingly sues for peace. Italy stays out of the war; much as it would like some meat out of the French carcass, the risks of naval war with Britain are too grave to contemplate.
The Germans would have sustained appalling losses, however, and still are bogged down in a costly war with Russia. The Blockade is pinching their economy. The result might well be hard terms for the French, but soft ones for Britain. The British will want to keep the Germans out of the Channel Ports and restore Belgium in some real sense. The tradeoff would be the dismantling of Liege and the other Belgian fortresses, the cession of Belgian Congo and much or all of French Equatorial Africa to create German Mittelafrika, additional French border cessions including Briey-Longwe and long-term occupation or dismantlement of French border fortresses in the Toul-Verdun line, annexation of Luxembourg, along with heavy reparations - and a free hand in the East and the Balkans. The British gain the fig leaf of splitting the German Pacific possessions with Japan, and pick up Togoland and Southwest Africa, given them at least the claim of having gotten *something* out of the war (along with a restored Belgium, sort of). The Ottoman Fronts end up status quo ante, the Arab Rebellion being stillborn, and the Germans look forward to new Ottoman markets to develop.
Meanwhile, the Tories are probably set up for a good run in power after the discrediting of the Liberals, and a rightist regime, perhaps even a Bonapartist or Bourbon, takes power in the rump of France, embittered at both Germany as well as Britain.
The Russian butterflies are a little harder to figure out, but it probably staggers to an expensive peace, with the loss of Poland part of the Baltics, and Nicholas forced to abdicate, giving way to an unstable constitutional monarchy facing deep unrest.