It all boils down to the initial deployment of the Staffel-B, AKA the 2nd Army. Deploying the 2nd Army against Russia (right from the start) would mean the Russians wouldn't have numerical superiority during their attack on East Galicia, and the Austro-Hungarians could stop their advance (at the very least) or even throw them back (behind the Sereth or even the border). Without the imminent need to reinforce East Galicia, Auffenberg's 4th Army wouldn't have to be suddenly diverted and it could completely encircle and destroy the Russian 5th Army at the Battle of Komarów. So A-H not only would avoid two disastrous defeats of OTL (Gnila Lipa and Rawa-Ruska), but it would also achieve a triumph on the scale of Tannenberg.
Later developments are harder to predict. The A-H 4th Army could occupy Kholm and some of its formations could be turned Westwards to flank the Russians at Lublin. With their positions threatened, the Russians might be forced abandon the city and withdraw to the fortress of Ivangorod. The arrival of reinforcements that IOTL were needed to replenish the badly mauled Austro-Hungarian forces could be used ITTL to create a new army formation on the left bank of the Vistula. This new Austro-Hungarian 7th Army, together with the also newly formed German 9th Army would then launch a coordinated offensive from the Krakow-Upper Silesia area. The A-H 7th Army would move against Ivangorod and the German 9th Army against Warsaw. IOTL both attack were performed by the 9th Army, with its forces split. ITTL Ivangorod would already be put under pressure from the South by the A-H 1st Army, the 7th Army piling on it from the West would increase that even further. Meanwhile, the German 9th Army would concentrate all its strength against Warsaw.
The lack of an attack from the North would probably allow Warsaw to defend againt the German attack, but Ivangorod would likely fall. That in turn, however would leave Warsaw vulnerable to the Southeast. At this point the Russians might just decide to abandon the Polish Salient altogether, however that's not a given, since the Autro-Hungarian forces would already be exhausted and overstretched. This, combined with the arrival of the Autumn rains (mud) would provide some breathing room for the Russians. The overall Russian might would be far from spent, and the continous flow of reinforcements would give the Russians opportunity to regain the initiative.
This is how I think things could develop, but
@Helmuth48 could probably offer a better perspective.