I tried answering the question earlier but I realized I needed to do some reading ("Information Structure and Sentence Form" by Knud Lambrecht, if you're interested), and the first thing is that, since these terms don't necessarily have constant, widely-accepted definitions, it's important to use the term as understood in the book. I mean, one definition of topic out there is it's the first element of a sentence, and that would trivially and unhelpfully answer your question
Anyway, I had a post that kept getting ridiculously long because there's a counterpoint to every point I make, and then a countercounterpoint, and so on, so to keep things short, I don't think you can tell in this case what the topic is (I agree with you about the focus, although there also seems to be some kind of contrastive focus between "others" and "Egyptians"). Both Ï„Î¿á¿–ÏƒÎ¹ á¼„Î»Î»Î¿Î¹ÏƒÎ¹ á¼€Î½Î¸ÏÏŽÏ€Î¿Î¹ÏƒÎ¹ (together with Î‘á¼°Î³Ï…Ï€Ï„Î¯Î¿Î¹ÏƒÎ¹) and á¼¡ Î´Î¯Î±Î¹Ï„Î± are topic-like in that the sentence could be presented as being about either one of them. Or to put it another way (since I'm more confident of being able to recognize topics in English), you could "translate" the sentence as either of:
1. Others live apart from animals, whereas the Egyptians live with animals.
2. The manner of living among other people does not involve animals, whereas the manner of living among Egyptians does involve animals.
which have different topics. The problem for me is that I can see either translation working in context, i.e. neither one sounds odd in terms of the what the topic is.
You could argue that á¼¡ Î´Î¯Î±Î¹Ï„Î± is less likely to be the topic because it's part of the "new information" of the sentence and the topic is usually "old," but if there were a shift in topic here, again, it doesn't sound odd to me.
I would say that as long as the theory handles the easy cases (where it's clear what the topic is), you let it tell you what the topic is in more difficult cases. And this seems to be a difficult case -- both my English sentences above have multiple words that are stressed. But to add, it seems to be generally true across languages that the topic comes first, or at least as close to the beginning of the sentence as possible. (Personally, I think that á¼„Î»Î»Î¿Î¹ÏƒÎ¹ is the topic here.)
(Although, what about the next sentence, which starts with á¼€Ï€á½¸ Ï€Ï…Ïá¿¶Î½ ÎºÎ±á½¶ ÎºÏÎ¹Î¸á½³Ï‰Î½? I don't know if that's the topic.)