The theory, which is proposed by a young professor at MIT, basically brings mathematics to a line of thinking that has been, with variations, proposed by a chemist (Ilya Romanovich Prigogine), a philosopher (the Cuban-born Alicia Juarrero—PDF), and a marine geologist, Eric D. Schneider, who wrote an important book, Into the Cool, on the topic with Dorion Sagan. What is said in this Quanta Magazine passage about the mathematician's theory is essentially what these other thinkers have been saying all along:
From the standpoint of physics, there is one essential difference between living things and inanimate clumps of carbon atoms: The former tend to be much better at capturing energy from their environment and dissipating that energy as heat. Jeremy England, a 31-year-old assistant professor at the Massachusetts Institute of Technology, has derived a mathematical formula that he believes explains this capacity. The formula, based on established physics, indicates that when a group of atoms is driven by an external source of energy (like the sun or chemical fuel) and surrounded by a heat bath (like the ocean or atmosphere), it will often gradually restructure itself in order to dissipate increasingly more energy. This could mean that under certain conditions, matter inexorably acquires the key physical attribute associated with life.
If you want to read Dorian Sagan's response to this post, go to here (which is a Facebook update by the cultural theorist Steven Shaviro). But basically life is a consequence of the deep structure of this universe. Change the values of this universe, and life will not happen. Something else might happen.