There are many parasite animals that do not breathe, e.g. the intestinal worms, because there is no air around them.
However those retain some features related to respiration, and they may breathe in some life stages, e.g. as free larvae.
The parasite described in the parent article is unusual because it has suffered an extreme simplification, deleting anything in its structure that is not strictly necessary for its lifestyle, so it has completely lost the mitochondria that enable respiration in nucleate cells.
Loss of mitochondria has happened in several kinds of unicellular eukaryotes, but this is the first example in a living being whose ancestors have been multicellular animals (which were related to jellyfish).
This is not surprising today, when it is known that the examples of evolution toward simpler forms are actually more frequently encountered than the cases of evolution toward more complex forms, but it was surprising in the past, when evolution was conceived like a ladder on which life forms with increasing complexity were placed, starting from the simplest and supposedly arriving to humans as the peak of evolution.
The title is as usual incorrect.
There are many parasite animals that do not breathe, e.g. the intestinal worms, because there is no air around them.
However those retain some features related to respiration, and they may breathe in some life stages, e.g. as free larvae.
The parasite described in the parent article is unusual because it has suffered an extreme simplification, deleting anything in its structure that is not strictly necessary for its lifestyle, so it has completely lost the mitochondria that enable respiration in nucleate cells.
Loss of mitochondria has happened in several kinds of unicellular eukaryotes, but this is the first example in a living being whose ancestors have been multicellular animals (which were related to jellyfish).
This is not surprising today, when it is known that the examples of evolution toward simpler forms are actually more frequently encountered than the cases of evolution toward more complex forms, but it was surprising in the past, when evolution was conceived like a ladder on which life forms with increasing complexity were placed, starting from the simplest and supposedly arriving to humans as the peak of evolution.
There are also Loriciferans, three species of which live in completely anoxic environments.
https://en.wikipedia.org/wiki/Loricifera#In_anoxic_environme...
The title is correct from a biochemical point of view.
At a celular level, the respiratory chain is a series of reactions that take place in and across a mitocondrial membrane. It uses Oxigen.
Edit: https://en.m.wikipedia.org/wiki/Mitochondrial_membrane_trans...
The article is more than five years old (from February 2020).