Once again I am trying to find about a story I read decades ago in translation (I do not remember the title in Italian, either). The main topic was a world where genetic engineering had starter producing "Fantasy" creatures (including satyrs, dragons) until for some reason tech-based civilization collapsed and the survivors were living in something that superficially resembles a Fantasy world.
If memory serves the book opens with a short scene where three "creatures" (including, but I am not sure anymore, a sort of werewolf) kill the family of the protagonist.
--- Some extra info as per requests in comments
a) It was probably a novel, definitely not a short story: it is difficult to say because it was published as part of a series that churned out lots of (translated) American and British works... but unfortunately in order to keep the throughput costant and make the page number more or less uniform, the editors often made extensive cuts to the original content (e.g. a couple of chapters completely removed from "The Shrinking Man"). For fellow Italians: Yes, I am talking of URANIA.
b) As per point (a): it is difficult to know the publishing date of the originals - Urania started publishing in 1952 but they often reprinted their content so in 80s you could still get an "Issue" with a story that had been originally published 10 years before, and whose American first edition was maybe even older. I think that the original was maybe from the 70s (I doubt that Genetic Engineering was really a common trope in the 60s), but I really have no idea.