Fundamentally, we should be able to agree that our emotional system emerged to trigger the individual as to important occurrences in the surrounding, to serve as a stimulant to a given type of action when environmental signals trigger those reactions because doing so is beneficial in some way to the individual (before social systems emerged there were individuals!). It is beneficial either by being outwardly pleasurable or by enabling us to avoid being eaten or being crushed by a falling tree.
When we look at the mammalian brain we see this hierarchy of emotional controls in the location of the machinery, deep in the mid brain associated with the hippocampus and amygdala...which it just so happens also form a critical tie point for the processing of long term memories.
I don't see this as a coincidence, I think the architecture of the brain points us toward the causation factors for the emergence of the guiding signals that I believe emotions are.
Stepping away from the mammalian brain let's look at a brain that is ostensibly very different from ours, the reptilian brain...and what do we see? that the differences aren't so "very" at all...in fact, architecturally the reptilian brain looks a lot like the mammalian brain minus the large fleshy neo cortex...it seems to be mostly emotional response and sensory signal processing regions. This hints at the ancient evolutionary factors that shaped emotional development in humans and lead us to a different conclusion from that reached in this study. Rather than be a tool that emerged to elicit cooperation (an actively evolved feature) it was a tool that emerged to promote survival (a subtle but important generality from "elicit cooperation" that may in fact contain such actions as a subset) it is only later that this mechanism was co-opted to serve social purposes (like eliciting cooperation) ...we have evidence to support this view since reptiles are not very social animals, though large numbers of some species can live together few species form the networks of social hierarchy that mammals do thus cooperation as a factor for emotional development has no formative environment in the very family of animals that were precursors to the development of the mammalian mind!
So there is a catch 22 to that theory that I can't reason passed, also it seems more evolutionarily expedient for a simple chemical system to reward or punish behaviors to benefit individual survival before the development of social coercion even evolved and goes in line with what we see as a major difference between Reptiles (and Amphibians before them) and progressively Birds (not as old as Reptiles) and Mammals (not as old as Birds). I think these questions for the emergence of particular traits are best answered by comparative anatomy of animals at different stages in the evolutionary race...I admit a bias to this as being an engineer it only makes sense as a method to trace back the origins of various structures in the biology but it affords a unique view into finding possible answers to these questions which absent the engineering and systems view would seem entirely subjective and difficult to answer.