The authors advocate using the Price equation to divide evolutionary change into selection and transmission bias components. They then claim that a high selection component makes a process more "Darwinian" and a high transmission bias component makes it less "Darwinian".
I think that this is a pretty strange approach. Darwinian evolution depends heavily on both selection and mutation. One without the other generally results in a short-lived evolutionary process. For me, selection and mutation are both core components of Darwinism.
The mutation rate is highly variable in the organic realm. For example, around Chernobyl, the mutation rate was massively elevated in the 1980s. Does this mean that organic evolution suddenly became non-Darwinian in Chernobyl? I would say "no" - harsh environments are perfectly compatible with Darwinism. However, this paper's authors seem to think otherwise.
Worse for this proposed classification scheme, the split between selection and transmission bias depends on how you partition the population into generations before applying the Price equation. High levels of selection at one temporal scale (e.g. parasite lifecycle) gnerally look like transmission bias at a longer temporal scale (e.g. host lifecycle).
The authors give an example of what they see as a cultural process heavy in transmission bias:
At the other end of the continuum is the case where the transmission component is large and the selection component negligible. Such a case would be where individuals were exposed to ideas, but deliberately or subconsciously modified them through their cognition to such an extent that the trait they exhibit bore little resemblance to the traits of the previous generation. Changes in trait frequency would then be best explained with reference to the (genetically evolved) transformative properties of the human mind, not cultural natural selection. Such a situation does not possess the usual paradigmatic features of a Darwinian processThe evolution of ideas within minds is not Darwinian?!? Many neuroscientists would disagree. See Keeping Darwin in Mind for the details.
The problem here is that the authors have chosen a high level of partitioning before applying the Price equation - namely, social transmission between minds. High level partitioning favours the "transmission bias" component of the Price equation. However a more appropriate level for studying the Darwinian evolution of ideas would be to see how ideas are copied within minds. Or maybe how neural spikes are copied as axons split. If you partitioned on these scales, you would see less transmission bias, and more selection.
If you want to base a classification scheme on the Price equation, you need to decide how to divide the entities you are studying into discrete generations. Unfortunately, most real-world evolutionary processes have copying on multiple different scales - and so the are many ways of doing this and it matters which one you choose. Unless you keep the subjective aspect of the partitioning scheme you are using in mind, using the Price equation in this way will just result in reflections of your preconceptions.