I'm not so sure that's actually a G, it looks more like a Z to me.
I looked in the 1914 Rangliste for anyone named Gaul. I only found 4 and none were in Leibgarde-Infanterie-Regiment (1. Großherzoglich Hessisches) Nr.115.
Oberleutnant Gaul, Füsilier-Regiment Prinz Heinrich von Preußen (1. Brandenburgisches) Nr.35 but on assignment with the Army of Japan.
Oberleutnant Gaul, Landwehrbezirk II Coln, 2. Aufgebot, a Feldartillerie officer.
Leutnant d. R. Gaul, Königin Augusta Garde-Grenadier-Regiment Nr.4
The very last one, though, might be promising. At least he's in a Hessian regiment and perhaps he started out in 115 and transferred later......
Leutnant d. R. Gaul, Infanterie-Regiment Kaiser Wilhelm (2. Großherzoglich Hessisches) Nr.116