didn't really pop up before the Judeo-Christian worldview spread all over Europe.

So was he talking the truth or just bullshitting someone whose knowledge of ancient civilisations is quite lacking?

I can't speak to his knowledge of ancient Civilizations, but his knowledge of the impact of the spread of Christianity is absolutely a little poop from a male bovine.

The western European view, which lasted right up to the early modern period, did not differentiate between "bad" and "evil". To paraphrase the great medievalist Gerd Tellenbach, distinctions between 'goodness' and 'justice' are at their core anachronistic when applied to the period.

The best example I can think of is in my own translation work. The Latin word iustitia, from which we get our modern English "justice", should almost always be translated as "righteousness" in medieval Latin. This truism only starts to break down post-1200 and even then in the secular legal sphere only.

I'm somewhat confused by his framing of the question. Certainly there was a conception of things as being bad and evil in antiquity, and certainly saying something is evil implies that someone can and should be judged. And what Nietzche had to say about pre-Christian morality is not exactly a useful source; Nietzche is first and foremost a philosopher with a very specific intellectual project in mind and his citations of Greek thought should always be understood as part of that project. I assume he had in mind Nietzche's On the Geneology of Morals which addresses the idea of a distinction between "Good" and "Bad" in history and concludes that the ancient conception of "Good" was firmly based on congruence or lack therof with aristocratic values. But he is trying to do a very specific thing, which is to argue that our value systems are historically grounded and therefore that our current value system-a product of historical circumstances not our own-is not something we should necessarily consider ourselves bound to(forgive me, philosophers, if I have misread Nietzche and feel free to correct me). Whatever his value as a philosopher is, his citations of Greek thought should be understood as intended to further that project and read critically accordingly as we would with any source.

EDIT: And it is true that at least some Near Eastern views did not differentiate between "Bad" and "Evil", although that has more to do with what /u/telkanuru is saying about the middle ages. For instance, the same Akkadian word, lemnu can refer to moral evil, evil things(demons, etc), bad things(bad weather, oil that has gone bad, etc), and the related word lemû in the Old/Middle Babylonian period the state of being unwilling(the Chicago Assyrian Dictionary has a highly amusing citation of the last use of the word in the phrase "The lion has been on the roof now for five days; they have thrown a lion and a pig to him but he is unwilling(lemû) to eat"). And certainly it is relatively trivial to point to examples of Gods punishing people for doing bad things; a particularly well-known example is the Hurro-Hittite "Song of Release" in which a description of how the city of Ebla was destroyed by the god Teshub for failing to release captives is proceeded by a series of moral parables analogizing bad behavior such as filial disloyalty or failure to discharge one's political responsibilities with various fantastical situations such as a cup cursing the smith who made it.