Looks like they deliberately use a conservative formulation of the "detrimental characteristics of a PD." Both players are required to have a dominant strategy, that leads to a situation where both are worse off than the optimal square.
A more expansive formulation would be something like "there is a Nash equilibrium that is not Pareto optimal." If the preference-ranking version of the PD is something like [[11],[24]][[42],[33]], this means that we'd also notice something interesting about the game [[22],[14]][[41],[43]], etc.
there is a Nash equilibrium that is not Pareto optimal
Like Stag Hunt.
What they argue is that mechanisms for producing mutual cooperation in games like your more expansive formulation but that don't match the deliberately conservative formulation might have been important in the evolution of cooperativeness.
Hannes Rusch argues that the Prisoner's Dilemma is best understood as merely one game of very many:
http://www2.units.it/etica/2013_2/RUSCH.pdf