I had glossed it, and the part where they make a surprise move to Kant, is ... not very convincing. The way they describe it doesn't make sense. It's not as if there's any proof that a "Whole" is life or vice versa. It's just one of their assumptions.

If we take their writing as some form of evidence for it, they claim children inherit your Parts, but that's not true. They also imply that Parts cannot exist outside the Whole, which is patently false when taken literally. But in the loose sense in which they seem to use it, I could totally see a piano as a Whole: keys, snares, hammers, sound board, it doesn't make sense outside a piano. Also, notable features of life aren't included nor implied by the concept Whole.

They also call Collectively Autocatalytic Sets an "established mathematical theory", but it's a mathematical property that can be true of some domain. It doesn't prove anything. There aren't any proofs involving that property in the paper either. Later they call it a "chemical reaction system," which seems to be more to the point, but there are so many of those.

It's just another idea, and not an original one either. Wikipedia: "Autocatalytic sets constitute just one of several current theories of life." That Autocatalytic sets by itself isn't enough to explain life may be a point, but there's no reason to assume they've found the magical ingredient in Kant.