In the context of heterotrophic theory of abiogenesis, what is an organism that eats other organisms called?
@Artem, it's been a while! Good to see you back on Biology.SE.

I doubt that any rigorous terminology exist to describe these "type-0 heterotrophs" living on "non-organismic" organic compounds.

You might be assuming that early organic matters can naturally be categorized as being fundamentally alive vs fundamentally non-living. It is more a question of philosophy of the definition of life than anything else but, to my experience, most authors who wrote about the definition of life tend to consider early life as a spectrum from "definitely not living" to "definitely a living thing". The existence of this spectrum questions the need for the terminology you are looking for.