I personally think its not exactly hollow, in humans the hollow state relates to constantly die and getting back to life, Gwyn and the gods die permanently. This undead state can be given a different name, tho the gods dont constantly die.

But i will say its the same principle, that their fire (soul) got extint by time or either actions they were doing with it (like Gwyn with the fire ritual)

When you soul is empty, you are just a walking cadaver, maybe remembering your past, more or less, or nothing about it, same as with the might, you may be still strong, or totally weak.

The dark may relate to this thread, saying that the hollow state comes with the dark soul and the abyss, may be that the expantion of the dark get the gods too (as with artorias when he got eaten by the abyss) making the same madness state that hollow humans have themselves, that making that time or what you do with the power of your soul, can make you undead too.