Unless this is a severe mistranslation, it seems to indicate a concept of ethics in terms of (1) actions rather than just character and (2) a moral law, which is exactly what Anscombe and Chappelle age saying the ancient Greeks didn't have.
I'm not familiar with the context of the quote, but it talks about a divine law, not a moral one. Today most people hold that the two are distinct: for instance if a divine law orders a fasting day, disobeying it is not a moral failure. (Otherwise morality would be indistinguishable from piety and obedience, and we wouldn't need a separate word.)
I think that if Chappelle (who says recent conceptions of ethics are very different from those of the ancient Greeks) and Anscombe (who says the same and adds that the key change between the ancient Greeks and us is that Christianity brought with it the idea of right and wrong as obedience to a divinely given law) were both right, we would not expect to find ancient Greek texts connecting right and wrong with obedience to a divinely given law. But in the Euthyphro we do find that; in the first quotation I took from the Euthyphro Socrates talks about piety ...
I was stunned to read the accounts quoted below. They're claiming that the notion of morality - in the sense of there being a special category of things that you should or should not do for the sake of the things themselves being inherently right or wrong - might not only be a recent invention, but also an incoherent one. Even when I had read debates about e.g. moral realism, I had always understood even the moral irrealists as acknowledging that there are genuine moral attitudes that are fundamentally ingrained in people. But I hadn't ran into a position claiming that it was actually possible for whole cultures to simply not have a concept of morality in the first place.
I'm amazed that I haven't heard these claims discussed more. If they're accurate, then they seem to me to provide a strong argument for both deontology and consequentialism - at least as they're usually understood here - to be not even wrong. Just rationalizations of concepts that got their origin from Judeo-Christian laws and which people held onto because they didn't know of any other way of thinking.