How are residuals used as new phenotype?
The residual is the level of error in a regression model, the lower the residual the better the model. Residuals cannot equate to a phenotype, it is actually the opposite if your regression model is trying to investigate a given genotype/phenotype(s) model. The residual in this case is the amount of infomation which the genotype/phentype does not account for, i.e. there are other factors resulting in your observations which you have not captured in your model. 

What I assume is that the regression model you are referring  is  investigating whether the residual is lowered by examining different gene combinations. The objective of a regression model is to lower the residual and I suspect that it is comparing the new residual against the old one. Therefore it is not being used as an input into a regression model but an assessment of its robustness.