I think this seems as if they worked out the fine print necessary to express that Bayesian networks are string diagrams in a suitable category. One morphs the bayesian net into what is called less frequently than deserved a factor graph, and this graph has to be the DAG they speak about. One can do some probabilistic thinking in the Kleisli Category of the Giry (-Lawvere) monad on Set, though here they speak at the more trendy Markov-category level. Numerically, the factors of the factor graph are tensors. Marginal probability of the joint output variables is given by contracting the tensors along the tensor network including the input variables, as expressed by the graph.