Granger's causality is a very restrictive and incomplete view of causality. Pearl's counterfactual system with do calculus is a more general way to think about causality. This SURD appears to be a souped up version of Granger.
Either way, Holland's 'Statistics and Causal Inference' paper (1986) is a nice read on the different frameworks for causality, especially in regards to Granger (&friends) versus do-calculus/Neyman-Rubin.
In case anyone else wants to take a look: