In particular (from a very quick glance!) it looks like they distinguish between nepotism and inherited human capital only by using a particular model. They have data on father-son pairs and the correlation between them in terms of publication record; and data on total number of publications of (a) academics' sons and (b) outsiders. They impose a model with just nepotism and inherited human capital and fit it to the data. I'd worry there might be other explanations for the observed patterns.