Shockingly, Williamson misunderstands what it is for an idea to be concretely empty. Concrete emptiness isn't a matter of being necessary, in the sense of obtaining in every possible world, but is rather a matter of obtaining despite having nothing to do with, how anything ever is with concrete reality.
This misreading is peculiar given that the distinction between concretely empty and substantial ideas is explicitly contrasted with the distinction between necessary and contingent ideas on pages 16-18!
Unger adopts the language of contingency and necessity and adapts it to the distinction between concretely empty and substantial ideas as follows:
A proposition is contingent, if, and only if, (the answer to the question of) whether the proposition is true depends on how things are with concrete reality. And, a proposition is necessary, if, and only if, (the answer to the question of) whether the proposition is true does not depend on, but rather it has nothing to do with, how anything ever is with concrete reality. (18)
Once this misreading is corrected one can see that the god counter-example isn't troubling for Unger. Whether or not there is a god is a concretely substantial matter since whether there is a god does make a difference to concrete reality: if god exists, then there exists the concrete individual god, if god doesn't exist, then there doesn't exist said concrete individual.
The first reading of analytic emptiness is probably right. An idea is analytically empty if it's concrete emptiness owes to linguistic or conceptual matters. In Williamson's words:
His picture seems to be that the truth or falsity of analytically empty ideas depends on semantic interrelations amongst our words or concepts rather than on features of the reality to which those words or concepts refer. For example, the truth of “All red things are coloured” is supposed to depend on a semantic relation between the word “red” and the word “coloured”, or a relation between our concept of red and our concept of colour, rather than on a relation between the red things and the coloured things. By contrast, the truth of “Napoleon died on St Helena” is supposed to depend on a relation between the man Napoleon and the island of St Helena, rather than between the name “Napoleon” and the name “St Helena”, or between our concept of Napoleon and our concept of St Helena. So if analytic philosophers’ ideas are analytically empty, they are asking verbal questions, not engaging with the concrete reality whose deepest and most general nature they were hoping to understand.
Williamson seems to think this neglects (i) that any sentences truth-value depends on the meanings of the words one utters, or the concepts one uses them to express and (ii) that "the truth of "All red things are coloured" does turn on a relation between the red things and the coloured things: that the latter include the former." (i) neglects that Unger is talking about ideas which are those thoughts a sentence expresses. Any way, of course, one construe an analytic idea as idea who owe their concrete emptiness only to conceptual or linguistic relations. (ii) is probably false. Consider the sentence "all red dragons are coloured." It is true, but it's truth doesn't turn on the relation between red dragons and coloured things, since there are no dragons.
In general the review doesn't grapple with Empty Ideas as much as one would hope.