The analysis starts with two maps of planetary albedo for Mars -- one from the 1970s and one from 1999-2000. Albedo is a fancy name for reflectivity; how reflective a planet is, and how that reflectivity is distributed on the surface, has an impact on the planet's climate.

These maps of reflectivity are then put into a climate model designed to simulate the climate of Mars. Using the albedo map from 1999-2000, the model predicts a surface temperature about 1 degree F higher than the model calculates using the albedo map from the mid-1970s.

A few important things to remember:

There are no actual long-term measurements of Mars' surface temperature. Thus, we have no idea if Mars is actually warming. The point of this paper is that changes in albedo, by themselves, will tend to warm the planet. There may be other, more important changes going on that overwhelm this one effect. We don't know.

It is a real stretch to argue that this albedo/dust-transport mechanism could be operating on the earth.

Hypocrisy alert:

You'll probably find that many of the people who embrace this result are the same people who say that climate models of the earth's atmosphere cannot be trusted. They probably don't know (or hope you don't know) that this an entirely a model-based study.

Finally, I cannot figure out why they used the term "global warming" in the title. It's as if they wanted to confuse people.