If we had a grid of cells where each cell was a number from 0-8, representing the number of neighbours, would that be equivalent to what these "links" are? I'm still finding it hard to understand.
links are first-class entities. Some rules have cell states AND links. Some rules treat cell states as topological metrics of neighborhoods or neighbors. See the detailed .md cited above for more details.
This is interesting and may reveal additional properties of certain class of CAs.
Yet, as some comments already stated what you do is basically study a subclass of multi-state 2D CAs where specific states from the finite state set have a specific meaning associated.
In general a CA is defined as a dynamical system governed by a local rule operating on the neighborhood configuration and yielding a new state. State set is typically finite. But the actual structure of the states can be anything you like. A valid state can be a tuple of a form (visible state, number of neighbors, sum of neighbors degrees, …). As the maximum neighborhood size is finite and the visible cell states are finite - there is a finite number of such tuples which constitute the state set on which a CA can operate.
Summing up - you are studying CAs in which your multi-state setup has some implied meaning. Still cool and interesting.
