This sentence could be written as "Are other animals that do not seem essential and that without whose activity we could not conceive life disappearing?" but this violates English end-weight principles. If you want more information, do a net search for "Definition and Examples of End Weight in Grammar." The article on the thoughtco dot com web site is meant for a general audience.

Salaam Ryota! Yes, "whose" refers to the "animals".

It is a badly placed adjective phrase. To make your sentences clear, place adjectival phrases next to the words they are intended to modify: “Are animals, without whose activity life could not be conceived, disappearing?”