This figure was arrived at by comparing the normal growth patterns of the United States population from earlier census and from that projecting what the population of the United States should have been had there not been a Civil War. As Bryan points out the high number to widows as heads of households, but also the unusual number of young women married to older men. While deaths during the war of soldiers are an easy number to obtain, the numbers who were critically wounded, or ill, or drug addicted and died before the 1870 census are not.
Another factor is that with the reconstruction governments there was much unrest in the south and many citizens did not report themselves to the census takers. Or they were in newly organized counties and just missed by the census takers.
The 1870 census was not a 'good' census in the south.