Us Vorta were going for Kauai while the Jems had their hearts set on Milwaukee (don't ask me to explain how those guys think).Best case scenario: the Vorta and Jem’Hadar, their gods being dead, decide they have no more purpose in life. They retire to Florida and/or commit suicide, the Alpha Quadrant powers are stabilized, and the Gamma Quadrant becomes an anarchic free-for-all rife with opportunity and peril.
Worst case scenario: the Vorta and Jem’Hadar, their gods being dead, decide (or are so instructed by the Founders prior to their death) that they have no more purpose in life except revenge. The war of conquest becomes a war of annihilation, with the goal of exterminating all solids indigenous to the AQ.
S31 probably figured that the Dominion was fighting all-out and ruthlessly regardless, so an all-out fight with a leaderless rabble would be an improvement.
My big question about the genocide plan was, did the writers really intend for S31 to win the war via attempted genocide? Because that sure looks like what actually happened in the story.