Another thing I want to add is that the study finds no impact on growth from changes within high incomes. It finds only impact on growth from changes between low and high incomes. This tells us that there is likely something else going on, that income inequality could be epiphenomenal.
The author jumps to the idea that redistribution could make things more equal. I know of no real theory for how it could. There is theory, however, for how redistribution could make things less equal.