Addressing this question the way it is phrased is quite challenging, primarily because our understanding of phenomena like nightmares or dreams is limited. The only defined understanding we have of these concepts pertains to humans, leaving uncertainty as to their relevance to other species. To illustrate, do nightmares require thought in a narrative format, akin to human thought? Are sensory inputs necessary? Are nightmares a product of certain consciousness aspects, or are they tied to any physiological mechanisms complementing consciousness? How significantly do nightmares differ, in their neurological makeup, from reflex actions or involuntary movements, or even from post-death phenomena such as rigor mortis? Is a nightmare an internal, subjective experience, like a theater play that one observes, or is it the mind making sense of certain bodily actions? And if one must observe a nightmare, who or what is the observer? A lack of precise definition for what nightmares even are immediately hampers our ability to answer such questions with any certainty.

It might be simpler to avoid subjective terms like "dream" or "nightmare" and approach this topic from a neurological perspective. It's evident that a neurological process is underway when an animal exhibits behaviors that resonate with its routine experiences (behaviors that exist within the semantic space of the animal's every day life). This is a relatively easier aspect to study and infer from; perhaps changes or activations in certain brain regions or neural nexuses responsible for the specific behaviors (recoiling in fear, locomotion, defence mechanisms) could provide insights. What triggers these changes? Are they spontaneous or do they originate from the nervous system? Do they result from cellular communication, presence of secondary metabolites, or some other factors? These are questions that we can begin to dissect and understand. With this approach, we can immediately engage in work and get answers.

On the other hand, it might be unhelpful to hastily anthropomorphize animals' experiences that appear similar to our dreaming. This assumption not only leaps to conclusions but also strays far from the realm where neurology or any other scientific discipline can provide guidance or some epistemology for verifying hypotheses. Furthermore, attributing human-like experiences to animals implies that we share the same experiences and invites our subjective bias. This not only introduces bias in scientific inquiry - something that by itself is unwelcome, but also limits our understanding of dreams or involuntary nocturnal behaviors. By looking at these phenomena from a human perspective, we risk overlooking critical aspects that could enhance our understanding of dreams (even in humans). To borrow from the term "standing on the shoulders of giants", we risk giving up a vantage point from these rigorously tested shoulders of science for a vantage point of the biased and subjective human condition. It's best to keep an open mind and consider both.

A helpful comparison can be drawn with our evolving understanding of life. Centuries ago, life was distinguished from non-living things based on factors like movement, growth, and size. Something that was alive was roughly between the size of an ant and a large tree, it had clear objectives in life, and generally speaking, it could move or contort itself to achieve the objectives. Decades ago, the criteria were self-replication and carbon-water composition. Now, we no longer confine life within these parameters. We are open to possibilities like silicon-based life, or life independent of water. We now have a broader understanding of life forms, considering structures like endosymbiotes alive despite their lack of self-replication. We also know a lot about entities like viruses, which we categorize as non-living, despite their resemblance to endosymbiotes. Today, we understand what is alive and what is dead not as distinct categories, but as a continuum, where on one end things are very vibrantly alive and on the other - inertly dead. This shift in perspective was possible once we managed to overcome human-centric bias. Scientifically, we could have made this discovery in the 18th century, a hundred or so years after the invention of the microscope and when they got reasonably good.

Similarly, in exploring phenomena likened to "animal dreams", we should probably adopt a first-principles approach, focusing on neurology and expanding our epistemology in the field as needed. By assigning human-like attributes to such phenomena, we risk introducing bias that could seriously limit our ability to comprehend what's going on, as it did with life for centuries. We jump to unhelpful conclusions from which we cannot reason - we can't ever verify the hypothesis that any instance like the one in the article is or isn't an animal dreaming, because dreaming is such a subjective thing we ourselves partake it. What is worse, we cannot define dreaming clearly because it is so far outside our scientific understanding.