I'm not following the discussion between the mentioned authors, but I just want to remark that Atheists usually don't consider Theodicy as a reason against the existence of gods.

Theodicy does not disprove a god, it just disproves either his benevolence or his omnipotence. You're free to choose.

Aside from that, Theodicy exists on two levels. General Theodicy is the obvious contradiction between death and suffering of innocents, and the existence of benevolent and omnipotent gods. There are several theological answers to that, all unconvincing - at least to non-believers. The 'stronger' Theodicy only applies to the Christian God. He's described in some bible sections as not only allowing, but even directly causing death and suffering. This is one of the reasons for the many different bible interpretations and God conceptions by Christians.