It is up to the person claiming that the system can be interpreted as a Turing machine.

"If we view these parts of the beach as the tape, and all crabs being in a state described by these rules as corresponds to halting, then this crab population can be seen as a Turing machine!"

This question has been explored thoroughly by the engineers at http://www.multivax.com

Be careful with definitions (sets of necessary and sufficient conditions) to any concept... counterexamples lie around the corner.