Have they proven their computational model is inequivalent to cellular automata? It is possible that the link rules could be translated into cell rules in regular cellular automata.
That said a different representation can always reveal new phenomena about an old model.
Depending what domain of cellular automata you're talking about this might be trivial -- just redefine the state space of the cell to also include which cells it is connected to, then all that information is available to use in update rules.
That said a different representation can always reveal new phenomena about an old model.