In summary, the traditional approach to the Drake Equation has been to assign fixed values to each polynomial, sometimes an ass-pull and sometimes based off of best estimates from the observable universe. i.e., "0.1 x 0.1 x 0.1 x 0.1..."
What these researchers did instead is try to account for the uncertainty of various parameters. They gave each polynomial values in the range of [0, 0.2] for example, ran Monte Carlo simulations on that, and came up with an empty universe 21.45% of the time.
To put it another way: we consider it a certainty that some worlds will bear life, and a certainty that some of that life will develop into intelligent civilizations, and a certainty that some of those intelligent civilizations will explore their local system, and a certainty that some of those explorers will develop into massive hyper-intelligent, technologically-advanced, galaxy-spanning species. But we haven't got enough information to be certain about any of those within any reasonable order of magnitude. The probability of any one of those may in fact lie so close to 0 that it solves the Fermi Paradox.
FWIW (and it's worth basically nothing), this has been my preferred solution to the Fermi Paradox for a long time now, and it's nice to have this paper to cite when it comes up in the future. I figured that it took Earth 4.5 billion years to produce humans, and humans are only barely space-faring at this point and I'm not certain we'll ever make it out of our solar system. Countless species have appeared and gone extinct in the meantime. It seems far from certain, to me, that evolution necessarily leads to intelligent life, and if I remember right, the latest thinking from evolutionary biologists supports this -- suggesting that modern human intelligence is largely accidental, rather than a byproduct of evolution.
The age of the universe would seem to suggest that there's been time for at least a few other worlds to develop intelligent life even at very slow, unlucky paces, but then again, at astronomical time scales the universe has been too violent up until recently to foster that kind of development.
The Fermi Paradox seems to have captured a lot of interest from people who like sci-fi and want to think about all kinds of fantastic ideas on why we appear to be alone. Is there a Great Filter? Is this a simulation? Are we in some kind of super-advanced stellar nursery? It's like nerd sniping (https://www.xkcd.com/356/) for a particular sort of nerd.