I shan't go into great detail, but the claims of the reviewer above (Nuenke) fail to adhere to the first rule of assessing another's argument; we should put it in the strongest form possible and then try to knock it down rather than assault a straw man. I would therefore recommend that the reviewer consult some of Barry's other work, principally Justice as Impartiality, to gain an understanding of Barry's conception of justice and approach this work in a more open-minded manner. In light of this work, the criticism that a theory of social justice is like a scientific hypothesis - something to be empirically tested - is is an unfounded criticism.
I do see why you might go in that direction and focus upon the empirical; because Barry does discuss several scientific questions, such as the nature of persons and their influence by genes and society when they are invoked to defend the moral argument of the 'Conservatives'. Importantly, I do not read 'the empirical' as fundamental to his theory of justice. Engagement with the science is, as I have alluded, principally part of a refutation of the 'right wing' ideal of personal responsibility that is brought out to shut down those on the 'left'. The moral is what is of most importance to Barry, he is after all a moral philosopher. To reduce this to a "personal worldview", however, is an impoverished understanding of moral argument and to this extent I would recommend further reading.
With this in mind, taking the book as a whole, Barry is beginning from several philosophical notions, such as the moral equality of persons and fair equality of opportunity. He then demonstrates the way in which several important assaults on these broadly shared ideals (namely personal responsibility and meritocracy, which themselves are often founded upon contestable and tendentious interpretations of scientific inquiry) are wrong and deeply damaging of society. To this extent, he is not arguing that, "people who are less well off feel terribly bad about their situations, and therefore we should make them feel better by redistributing the wealth." To be sure, wealth does improve a persons' well-being; why would any of us want wealth if it didn't improve our well-being? Importantly, however, Barry is arguing that in light of the moral equality of persons and the lack of a legitimate reason to depart from pretty strict equality (due to the failure of personal responsibility and meritocracy), we should redistribute wealth aggressively. Importantly, this will not only improve the lives of the worst off as the reviewer's quotation suggests, but, as he details in the discussion of "positional goods", this will also improve the well-being of those all the way up the economic ladder. Redistribution of wealth improves the lives of both the poor and the better off.
I would recommend a more careful and more sympathetic re-reading of this book. It is more political and less philosophical than his other work (it is more like 'Culture and Equality' than, say, 'the Liberal Theory of Justice'), but nonetheless, substantive and well reasoned. It touches upon several important issues, such as the 'cult of personal responsibility' and meritocracy, and effectively engages with them. On these grounds alone, persons trying to navigate the contemporary political scene would gain much from this work. More-than-this, those interested in the philosophical component of Barry's work will also find this a fruitful read. It supplements 'Theories of Justice' and 'Justice as Impartiality', and when taken with these two, provides valuable insight into Barry's thinking. This is an valuable work that the reviewer above fails to fully appreciate.