Although I agree with author up to this point, he is not necessarily correct on this point. The moral subjectivist here is not necessarily acting as if his ethic was objectinvly binding on others, rather, he is just imposing his will to achieve his subjective desires. He doesn't necessarily believe this will is "objectively valid and binding on others", he just feels no compunction in forcing others to do as he wishes becasuse that's what HE wants and he sees no reason not to. Objective ethics of "right" and "wrong" don't enter into it at all, just the personal desires of the actor - he's forcing others to act this way not because he thinks it's "right" but becasue it's what he wants. That's all subjective "morality" leaves, personal preference and social convention.
I understand but this does not necessarily become an either / or situation it can also be a both. IOW the atheist could both think it is right, and do it because that is what he wants.