After rereading the article with a little more care, I was struck by the little space dedicated to the possiblity of an emergent time (as opposed to emergent space) and by the perplexities this possibility seems to raise according to the author. That is because from the LQG side of the quantum gravity research, Carlo Rovelli has argued for a long time that time is not a fundamental feature of the world but an emergent one, and for him this has a very precise meaning. A slogan repeated a lot in his book (available online in a draft version) says "Dynamics is not about evolution of observables in time, but about the correlations between different observables". His idea is that the objective of mechanics (classical or quantum) is prediction of correlations between observables, and that only in special cases there is an observable "t", measured by a "clock", that is unaffected by the other variables. Rovelli has put forward an hypothesis about how the appearance of "time" as a special variable emerges from an underlying timeless world, the Thermal Time Hypothesis, in which I am interested because it has surprising connections with my present work (through this paper), a story I will explain some other day.
I don't know if Rovelli's opinions on the subject are dominant in the LQG community, but I find it interesting that apparently from the point of view of string theory space seems to emergent from other more fundamental entities but the emergent quality of time is poorly understood, whereas from the LQG point of view space is built from irreducible "atoms" of space (in spin network models) but time seems to be understood as emergent, at least by Rovelli. Looks as if more dialogue between the two communities is needed...