That's what I always thought too. But according to the article, you could build up an atmosphere, and it could last tens of thousands of years. I'm in no position to evaluate if that is true or not, but that's what the author says.
Before being stripped away by solar wind.
Basically you'd have to have a periodic (frequency depending on the size) infusion of gases to replenish the atmospheric gases that are being constantly stripped away. That means, basically, crashing a comet, or parts of a comet, onto the Moon periodically to replenish the gases. Now, we know from Earth history, that crashing a comet onto the planet is highly detrimental to any biosphere/ecosphere that exists on the surface due to the terrible consequences of the force of the impact, atmospheric contaminants raised by the force of impact, and disruption of the environmental conditions that allow life to flourish. So having to crash a comet onto the lunar surface every few years, or few decades, perhaps few centuries... that's thousands of times the rate at which comets have impacted Earth and created catastrophic damage to the ecosphere, either regionally or globally. Perhaps with monthly infusions of gases via small cometary fragments, too small to reach the surface or incapable of creating giant impacts and their aftereffects, it might be possible, but such would require an ENORMOUS and CONTINUOUS expenditure of money and effort to maintain.
AS previously mentioned, this does NOTHING to abate the radiation problem. It will be impossible to set up an ecology on the surface when it's bathed in radiation, unless you breed specifically engineered organisms to withstand the radiation environment.
Then there's the fact that the gravity is so much lower than Earth... Lunar gravity is 16.6% that of Earth, and Mars gravity is 33% of Earth's. That means, with less gravity pulling on the mantle of gases making up the atmosphere, that it's going to be MUCH lower surface pressure than on Earth... The depth of the atmosphere (how many miles it extends above the surface) and its pressure gradient are determined by two main functions-- the mass of the gases making it up (specific gravity, or density of the constituent gases in the atmosphere) and the gravitational force pulling down on those gases to overcome their natural collisions between molecules (which creates what we sense as "pressure"). With less gravity, the gases aren't going to be drawn as strongly to the surface of the planet, and their natural collisions are going to keep pushing them apart more effectively than Earth's higher gravity does... meaning the atmospheric pressure at the surface will be much less than at Earth, due to the gases "spreading out" due to lower gravity, creating less pressure. It will also mean the atmosphere will have a lower "pressure gradient" than on Earth, meaning it will be much thicker despite being smaller and lower pressure than Earth... (smaller due to a lower volume of gases surrounding the Moon, which is 1/4 Earth's diameter, and Mars, which is 1/3 Earth's diameter-- Earth's atmosphere consists of a shell of gases roughly 60 miles thick surrounding the planet, IOW, a hollow ball with the inner surface being the diameter of Earth itself, and the outer surface being roughly Earth's diameter +120 miles (60 miles on each side). The volume of such a hollow sphere is easily calculated mathematically. Earth's atmospheric standard pressure is 14.7 PSI at sea level, with 90% of Earth's atmosphere existing below 20 miles altitude, in a decreasing pressure gradient from the surface to the "edge of the atmosphere". In reality Earth's atmosphere extends far beyond 60 miles, in a region of increasingly thinning gases of the exosphere extending up at least several hundred miles-- regions that we would consider a 'vacuum' but in reality there is still stray atoms of gas that DO create drag-- which requires that ISS, Hubble, and anything else up there in "low Earth orbit" (LEO) receive periodic reboosts to overcome this drag, especially "fluffy" objects with lots of surface area for their mass, like hollow space stations and space telescopes, which lose momentum faster than smaller, denser objects like satellites with no or very little "empty volume" inside.)
So any "atmosphere" we create around the Moon or Mars will, by definition, be much lower surface pressure than Earth, and get thinner slower as it goes up, meaning it will be much "thicker" than Earth's atmosphere... (maybe extending up to well over 100 miles instead of essentially tapering off to "nothing" (so to speak) above 60 miles as Earth's atmosphere does. The Moon's lower gravity will be even worse in this respect than Mars, since lunar gravity is half Mars gravity...) Space suit pressures are commonly operated at 5 psi, roughly 1/3 the pressure at Earth's surface. Even establishing and maintaining a pressure on the surface of the Moon or Mars of 5 PSI will be an enormously difficult undertaking. In addition, just because you have an atmosphere, doesn't mean you can establish an "ecology", due to the fact that most plants and animals need a higher pressure to flourish... we can see "timber lines" above which trees won't grow and other ecological divisions based on temperature primarily on temperature, pressure, rainfall patterns, and other ecological and environmental factors.
Then there's rainfall... Even on Earth, with a "thick" atmosphere (high surface pressure, relatively speaking), areas without rainfall are largely devoid of life, what we call "deserts". For an example of what the Moon or Mars would look like without rainfall, look at the Atacama desert in South America... it's the driest place on Earth, and essentially devoid of life. Dry at the Atacama is, it's practically swimming in water compared to the surface of the Moon (and perhaps Mars) without rainfall. Cold, dry air cannot hold much water vapor, and at lower pressures this is especially true. So establishing reliable climatic conditions capable of producing sufficient rainfall to support "natural ecologies" without some form of irrigation will be difficult if not impossible.
Add all this together, and it looks like there's a lot of stuff that's been overlooked or "waved off" in the dreams of terraforming and establishing ecologies on the Moon and Mars...
Later! OL JR