My first reading is that it's kinda a like a Christopher Alexander process take on what comprises life; eg: "The specific molecules in your body aren’t that old, but the lineage of these objects being reconstructed goes back that far. From this perspective, we should think of ourselves as lineages of propagating information that temporarily finds itself aggregated in an individual. We are our history. So, we’re reframing life by thinking about it as a temporally extended structure. It’s a lineage, not an individual."
"Our key argument is that if something is hard to make, and requires many steps, then you’re not going to see an abundance unless there was a selected pathway that makes it. In a meteorite, molecules with high assembly level are produced in such small amounts by random processes that they are undetectable. But if an object is alive, then selected pathways can reuse parts from the object’s history to make an abundance of structures with high assembly. That’s the only way to traverse this exponentially growing space of all possible things and so explain the existence of life. You have to trace out historically contingent paths, and we’re trying to find out what the minimal number of steps needed to get there is."