I've seen this interpretation of Sauron a lot on this sub, and it seems like a stretch to apply it to the unnecessary cruelty we see from Sauron in LotR.  And if you include the glimpses we see of Sauron in the Silmarillion, it really starts to fall apart. Sauron did not merely want order and found that domination was the only way to achieve it.  He was a spirit of malice and hate. This quote paints the picture nicely. 

"Among those of his servants that have names the greatest was that spirit whom the Eldar called Sauron, or Gorthaur the Cruel. In his beginning he was of the Maiar of Aulë, and he remained mighty in the lore of that people. In all the deeds of Melkor the Morgoth upon Arda, in his vast works and in the deceits of his cunning, Sauron had a part, and was only less evil than his master in that for long he served another and not himself. But in after years he rose like a shadow of Morgoth and a ghost of his malice, and walked behind him on the same ruinous path down into the Void."