I would argue that it is more "primordial". After all, computation is first and foremost a human activity, generally performed using pen and paper, which involves a good deal of rewriting (computers were originally people). The machine only came later as a way to simulate this human activity. Its meaning is entirely contingent on the primordial notion. It have no meaning on its own.
Of course term rewriting has a meaning of its own, it is at the same time more meaningful and simpler as any other form of computation.