For anyone who is interested, the map of the German
First Army advance on 25 August 1914 is shown below reoriented North-South:

Legend: HKK 2 is akin to a cavalry corps; R = Reserve; and ID = Infantry Division
It shows that the advance was oriented to trap and eliminate the BEF, which was thought to be in the area of Maubeuge. IX Army Corps was told off to screen Maubeuge on its western side. III and IV Army Corps swept around to reach the Sambre River, where they made contact with German
Second Army. HKK 2 was trying to get below where the BEF was thought to be when they ran into BEF II Corps unexpectedly next day. Having discovered the mistake about the BEF on the evening before the Battle of Le Cateau, IV Army Corps proceeded south next day and made contact with BEF II Corps. III Army Corps was following on behind.
All the while that III and IV Army Corps were heading towards the Sambre, they were clashing with rearguard elements of BEF II Corps. The two German corps passed across the back of BEF II Corps retreat but never realised the significance of the clashes. This highlights how hard it was to know that a major force was relatively close by. Certainly the BEF forces would have been visible to a wargamer commanding the German forces but not to his/her real life counterpart on the ground.
This brings me to the influence of the Great German General Staff (GGGS) on operational planning and execution. Army corps and infantry division HQs all had generals in nominal command. The planning and execution was performed by the attached officers of lower rank but higher command status from GGGS. Usually there was agreement between the generals and GGGS staff. If disagreements arose (such as von Kluck's insistence on trying to continue attacking the French on his exposed right flank near Paris) then GGGS had the ultimate authority.
A goal of GGGS (and its equivalent in the French and British armies) was to ensure that the million man armies operated as a synchronised whole. They coordinated the routes of march, for example, to ensure that divisions remained in their allotted sectors and maintained the timetables.
Robert