Hi Helder!
Good question about why I'm using discrete and finite systems formalize causal emergence, rather than analog concepts (like feedback, etc). The first reason is that this allows supervening scales to be easily defined and modeled. For instance, one can generate the full space {S} of possible supervening descriptions of any particular system, and then search across that space, as we did in Hoel et al. (2013) "Quantifying causal emergence." Another reason is that information theory, such as mutual information is most often represented as between two finite and discrete variables. A third is that the causal calculus of Pearl is also often represented in terms of Markov chains. So showing how these all can be synthesized is much more direct in these types of systems (applicable to things like cellular automata, etc).
But this doesn't mean linearity / nonlinearity and related concepts doesn't come into play, it just wasn't addressed in this essay. See Hoel (2016) "When the map is better than the territory" of a discussion on how symmetry breaking is critical for causal emergence.
Thanks so much for reading!
Erik P Hoel