You may have resolved this now by talking to Richard (who knows more about this than me) but, in case you haven't, I'll have a shot at it.

First, the distinction: Richard is using rigid designation to talk about how a single person evaluates counterfactual scenarios, whereas you seem to be taking it as a comment about how different people use the same word.

Second, relevance: Richard's usage allow you to respond to an objection. The objection asks you to consider the counterfactual situation where you desire to murder people and says murder must now be right so the theory is extremely subjective. You can respond that "right" is a rigid designator so it is still right to not murder in this counterfactual situation (though your counterpart here will use the word "right" differently).

Suggestion: perhaps edit the paragraph so as to discuss either this objection and defence or outline why the rigid designator view so characterised is not your view.