"DNA is extremely important, but it makes no sense if [it is] not in a cell, in an organism, in an ecosystem. Other interactions are at play, and this application of algorithmic information cannot capture the extent of that complexity."
Completely mischaracterizes the research (Zenil et al.). They are looking at networks evolving over time of interacting elements. Such elements are genes but networks can also be metabolic or signaling and everything they say still holds.
The subsection about chasing dynamic evolving targets even addresses the question of ever-changing environments that have some raised here. So the approach is way beyond treating life as 'DNA' but even so, I doubt anyone would object about the power of CRISPR-CAS9 only because it targets DNA... DNA is still the most fundamental element of life and other tend to embrace mysticism and are quite cartoonish about life.
Anyway, my recommendation is, do read the paper.