This works for 19 animals: tiger, lion, elephant, zebra, ape, sheep, duck, rooster, turkey, owl, cat, pig, cow, dog, moose, raccoon, horse, humpback whale, bowhead whale.
Google uses MP3 files like www.google.com/logos/fnbx/animal_sounds/cat.mp3 for playing animal sounds, so they work in almost any modern browser that supports HTML5 audio. For some reason, turtles are no longer available in the card, but you can still find the MP3 file: www.google.com/logos/fnbx/animal_sounds/turtle.mp3.
An article from Indian Express mentions that "the sounds have been recorded from live animals" and the feature works for "the top searched for animals in Google and animals with some of the most iconic sounds". It was supposed to be launched back in January, but Google announced it in March.