While it's true that "emergence" has become a buzzword, but there are different kinds of emergence, and I personally think the fact that there are no fundamental degrees of freedom is a good trait.
I see two ways of emergence;
(1) from a fixed set of complexions, or a fixed "fundamental" state spaces, emergence of a particular structure is in a sense reorganisation; like order "emerges from chaos" by self-organisation of a given, but fixed set degrees of freedom/microstructures (I use these as synonyms as it just depends on wether we consider continuum models or discrete ones; their purpose are the same).
(2) if we add ontop of the first idea, that the representation and description of this process can only "live" on the inside; ie seen from the point of view of an inside observer. Then we get also the peculiar thing that the state spaces and the VISIBLE degrees of freedom can never be fixed or fundamental. They are evolving.
So in(2) we have emergence w/o fundamental mictrostates or degrees of freeom by evolution relative to some existing microstructure. (which one in the generalized sense may call a background) but that this is still evolving. But the FULL evolution can never be predictable by an inside observer and thus can never be falsifiable. Thus I think this isn't what we should seek, we should instead try to find the best possible inside description, and try to separate the decidable from the undecidable.
I don't think verlinde goes far enough, but the idea he has that space emerges not from some fundemantal degrees of freedom, but by expanding on an existing piece of space, fits to the principal reasoning I agree with. The point would then be that at some level or horizon each observer simply reaches a point where this evolution is undecidable and unpredictable, that that's it.
If you think that this is really how nature indeed works (not the built-in locality in this view) then must not let our desire of seeking eternal truth and timeless forcing laws, blind us and prevent progress.
As I see it, in this picture, combined with a generalized entropic idea, even the ACTION form, governing the expected action in a given microstructure system (at an instant of time) has emerged from a much simpler action. In this sense I don't think CDT goes far enough either. The Einstein hilbert action should be emergent too (from first principle entropic flows) along with emergence of space, and I think THIS could be possible to understand.
Except I haven't read the paper but I fully share the general ambition and view that the entropic reasoning can be applied to all interactions. This is exactly what is implicit in what I've labelled "rational action". The rational action is pretty much a random action, but guided by the existing state space. IF you pick a "random perturbation", one will generally get a probability distribution that looks something like the exponetial of the negative information divergence. This unifies action and entropy notions into a generalized probability framework, and if we combine this with memory transformations (as different compressions) non-trivial actions will appear; in particular will be break classical logic as expressions such as A an B; or A or B, when A and B refers to different spaces, which are related by mappings but that are still at the upper level unified by transforming back to the original set, and thus we get a real number assosiated to it (probability).
Moreover in the discrete picture, this may be coutnable so that one can start from zero complexity and classify interactions. (Here string theory is "similar" except it start from some unclear idea of a "string" in a background- which is also part of the reason for the landscape; otherwise it has similar traits).