Unique means one of a kind, that there is no other exactly like the thing being described as unique. In this sense, "uniquely Singapore" is truly meaningless advert-speak. Every place is unique unto itself, as there is no other place which is that place. Both Iceland and Hawaii may be islands, both the Mojave Desert and the Sahara Desert may be dry, both Tibet and Colorado may be mountainous, but each of them is unique in that each of them is the only them.