ok, I should admit that I am struggling here, as I am reading up on this definition for the first time.  
 Help is appreciated. What is clear is that the article was completely mistaken.  
 The coefficient isn't even defined in terms of genetics, but in terms of genealogy. It can be calculated precisely if the full genealogy is known, never mind genetics.  
 Of course it is intended to still make a statement about genetic relatedness, but that's not part of its strict definition. 
 It is intended to describe breeding processes of mammals, so I am not sure it can even be meaningfully applied to hymenoptera genealogies. 
 I have so far looked up the 1922 definition of r. It involves summing over all paths in the full genealogy. The thing being summed are path coefficients, and these path coefficients are in turn defined in terms of the inbreeding coefficient. As the inbreeding coefficient isn't defined in the 1922 paper, the reader just being referred to the 1921 one, I have not so far been able to supply the full definition.