In a trivial sense, this is true. The sentence ‘We want to make the poor poorer’ does not appear anywhere in The Spirit Level.
But the Spirit Level authors say explicitly that their ultimate goal is the establishment of a Steady State economy, which means forcibly ending economic growth. Why? Because they believe that beyond a certain threshold, economic growth brings no additional benefits (‘Further economic growth in the developed world no longer improves health, happiness or measures of wellbeing’, p. 218-219), but imposes immense costs, by fuelling global warming. Indeed, there are passages which one could read as a plea for economic shrinkage: ‘Carbon emissions per head in rich countries are between two and five times higher than the world average. But cutting their emissions by a half or four-fifths will not be enough: world totals are already too high and allowances must be made for economic growth in poorer countries’ (p. 217).
The authors also reject the notion that climate disaster can be avoided by increasing energy efficiency: ‘Imagine that a new generation of car engines is introduced which halve fuel consumption. Driving would then be cheaper and that would save us money, but it is money which we would almost certainly spend on something else. We might spend it on driving more, or buying a bigger car, or on more power-hungry equipment – perhaps a bigger fridge-freezer. […] As cars have become more fuel-efficient, we have chosen to drive further. As houses have become better insulated we have raised standards for heating […] Because energy-saving innovations mean that we can buy more, they are like economic growth’ (p. 223). Note that in the authors’ view, this is a bad thing.
Regardless of what you make of The Spirit Level – you cannot pretend the book was a manifesto for improving the living standards of the least well-off. How could it be? If you believed material consumption was nothing else but a self-obsessed status hunt – and the sub-chapter on ‘consumerism’ shows that this is exactly what the authors believe – then why would you want anybody to have more of it?