I don't know the answer to your question, however, my guess is that Arabian perfume companies (and probably most western ones) don't test perfumes on animals. They simply mix synthetic ingredients that are produced by aromachemical companies and are known to be safe. However, said aromachemical companies have, in the past, tested their molecules on animals to establish safeness before they started marketing them. And this is true for Amouage as well. probably what the statement means is that the molecules used are not tested on animals now. Of course, they might have been 10 years ago when said molecules were being developed. But this is my interpretation.
As for animal derived ingredients, they are absent from modern perfumery simply because they would be prohibitively expensive. Musks, civet and ambergris have been substituted by synthetics. Perhaps only a handful of really expensive upscale perfumes, such as some of the superexpensive attars of said companies, do contain a touch of true ambergris, but certainly not the regular ones. (Civet is not much used in arabian perfumery, and animal musk doesn't exist anymore, simply because said deers have been nearly driven to extinction decades ago).