The verb to famish
here means to make thin.
The Lord intends to ravage the land so that the inhabitants will lack food to offer to the idolatrous gods. They will be diminished and withered to nothing because God’s judgment will take away the people of the land, and thus the gods will lack attention and food.1 The Lord will defeat all evil. And with the gods destroyed, the people would then begin to see the real rather than the counterfeit.
2
11 The LORD will be awesome against them; for he will famish all the gods of the earth, and to him shall bow down, each in its place, all the lands of the nations.