Although important, Moscow is not as vital as Petrograd, that is the center of Imperial Russia, threaten it or take it and I believe you seriously if not mortally wound Russia. In an "East First" scenario I think more pressure gets put on moving towards Petrograd could force Russia out of the war earlier. In OTL, I am thinking of having Falkenhayn redirect effort East versus attempting to break the French, instead he sweeps Romania and drives into Russia, seeking a decisive battle that cripples the Russian ability to sustain the war, opening the door to a negotiated separate peace. I am uncertain if that can result but the payoff for Germany was breaking Russia, it had space but really not time, its war effort relied too much as Germany spreading thin and prioritizing France, but why? The Western Front was deadlocked and on the defensive the French held all the cards, the more "natural" German move was to be offensive where posible and that still to the East. If one can get Germany to hold defensive in France, I think the war is far better for Germany being fought Eastward, Russia facing a steady onslaught threatening Petrograd might fold soon enough to release the Germans from the deadly drain of a two front war.