My interpretation is fully deterministic in the same sense that their was. Probabilistic is meant in the "sum over histories" sense that multiple histories yield the same present, so you can't reasonably pick just one and say "That's what came earlier", but you instead have a spread of probabilities of linkage. I interpret that probability as the strength (weight) of the link. From each past the probabilities to all the futures it links to sum to 1. Similarly from each present the probabilities of all the pasts it links to sum to 1.
The difference between out models is that EWG, at least in the presentation that I read, only considered forwards (toward the future) links. I see no reason to believe that this is a correct interpretation. (I'm not sure about chronology, but I believe the EWG model was created prior to Feynman's Sum over Histories approach being derived. This difference is probably the result of that.)