The battle between Hell and the Abyss, in the short term, actually has no true meaning of victory.
After all, for both sides of the war, what they really aim to do is to completely engulf the other and thereby become the 'sole' entity again, not an easily achievable goal. Under such circumstances, once the collision of power begins, it likely won't stop, not even with the death of those Demon Gods who invaded the Nine Hells. Unless one realm is utterly destroyed, the war will never end.
Therefore, what the Serpent of the Central Court refers to as 'accomplishing its mission in one fell swoop' does not mean ending the war itself but rather ensuring it progresses in a way that better serves the interests of the Nine Hells. After all, for the weaker side, the most important thing is to control the intensity and scale of the conflict.