The winning objective is very simple: Kill all members of the opposing team(s), including NPCs if there are any.
In some Annihilation matches, teams do have a Resurrection Shrine tended by a Priest. The Priest will resurrect all dead party members every 2 minutes. To win, the opposing team must be dead and their Priest killed as well. The Priest cannot be resurrected.
Some Annihilation matches feature Obelisks that can be used as a tactical advantage to beat the opponent team even faster.