If true, and it seems probable that replicating chemical systems do actually evolve in a non-random fashion, then it should stand to reason that microbial life is common. If life was the product of random chemical interaction - as they state - then the chances of increased complexity would be virtually zero.
One of the authors they cite in the paper, Kauffman, has postulated that the emergence of life should be a general phenomenon due to its thermodynamic favorability, a somewhat counter-intuitive result. His argument basically says (simplified drastically): For randomness to result in life would require more time than has elapsed in the universe thus far (and a lot more; I can't remember the number off the top of my head, but I believe it's orders of magnitude). Therefore, it is mathematically impossible for life to have resulted from randomness. If not randomness, then it must be thermodynamically favorable for life to emerge.