Ruminants deplete the vegetation on the land, leading to erosion caused by wind and water, which gradually erodes the top layer of soil, leaving behind only large rocks.
There are ruminants in plenty of other places without the land becoming inhospitable to most plants, though, so that's not a sufficient explanation (although I can clearly see how it contributes).
"The authors analyze archaeological and ecological evidence to understand the relationship between human populations, goat herding, and land degradation. They argue that the widespread adoption of goat herding practices played a significant role in the process of desertification. Goats are known to be browsers, preferring to consume a variety of vegetation, including shrubs and trees. This selective feeding behavior, combined with the increasing human population and expansion of agricultural practices, led to the overgrazing of vegetation and subsequent soil erosion.
The paper highlights that the degradation of vegetation cover and loss of soil fertility had cascading effects on the ecosystem. Reduced vegetation cover resulted in increased exposure of soil to wind and water erosion, leading to the expansion of arid and desert regions. The loss of vegetation also had a detrimental impact on biodiversity, as many plant and animal species dependent on these ecosystems faced habitat destruction and population decline."
Are you suggesting that ruminants transport rocks to the site?