As far as this paper goes, the most interesting implication isn't mentioned in the phys.org article. It seems to me that main idea of the paper is to connect the development of life to the cosmological evolution of the universe. We find that we live in a somewhat special time, when the universe is just starting to be dominated by dark energy after having been dominated by matter since ~300,000 years after the big bang. Anytime you see that we live at some sort of a special time, the Copernican principle leads one to wonder if there is some underlying reason for this.
The main argument of this paper is that as the universe becomes more dominated by dark energy, the expansion of the universe accelerates and this shuts off the flow of gas onto galaxies. As galaxies stop accreting matter, star formation slows, making it less likely that life will develop in the far future. However, low mass stars are more abundant and have a longer lifetime, so even if it takes a longer time for life to evolve in that environment, it's still, on balance, more likely that life evolves around low mass stars in the near future ("near" still being tens to hundreds of billions of years). So we would expect that the typical life form will evolve around a low mass star, far in the future. Thus, life on Earth seems to have developed early, but maybe not unusually so, and it's maybe not a coincidence that we happen to live a little after the time at which the universe became dark energy dominated. I would file this away in the "interesting if true" category.