Why wouldn't they feel pain? It's such a superior attitude to even consider that only humans could feel pain. It's also obvious that any complex organism feels pain... It the most basic evolutionary protection mechanism. Anything that didn't feel pain would soon be evolved out.
Even the featured article puts pain in quotes and is like, “for simplicity, we’ll call it ‘pain’” So actually it’s not obvious that animals perceive the world as we do. Maybe you can only generalise our experience to warm blooded vertebrates.
No, animals don't perceive the world as we do but it's not stretching things at all to say that they do (have to!) register some of the basic realities of life such as warmth, cold, pain (i.e., 'this is bad - something's not right and needs to be sorted') and absence of pain. The nuts and bolts of this are bound to be similar or identical given that we share a lot of basic biochemistry with all life forms. For example the citric acid cycle (a fundamental engine for energy production) operates together with its associated pathways universally in plants and animals.