This type of herbivory is probably from feral livestock, especially donkeys.
There is video footage of guanacos eating flowers off of cacti in the Atacama. For example, an image capture of a Getty Images video:
Credit: BBC Natural History
This type of florivory has been documented in related species of cacti as well (e.g., see Gomes et al. (2016)1)
However, I could find little evidence about guanacos eating the trunk of these cacti (especially to the degree you describe).
Actual herbivory of Echinopsis cacti has been reported in multiple publications. For example, Peco et al. (2011)2 cite feral livestock as a major source of herbivory in columnar cacti in South America:
Columnar cacti are an important feature of the arid “cardonal” landscape in South America. The predominant columnar cactus in the southern zone is Echinopsis (=Trichocereus) terscheckii. At some sites, the species suffers considerable trunk damage, attributed in previous studies to feral livestock grazing (donkey and cattle).
In a previous study we found that damage intensity on Echinopsis terscheckii trunks correlated with abundance of livestock dung in their surroundings, but not with the abundance of guanaco dung (Lama guanicoe) (Malo et al., 2011; Novillo and Ojeda, 2008). Futhermore, E. terscheckii was found in summer or winter donkey diet but not in guanaco diet in the study area (Reus pers. comm.). Direct observation of donkeys feeding on columnar cacti suggests that this species is the main cause of stem damage
See this National geographic video explaining how camels and other related animals handle eating spiney cacti. (Specifically, they accomplish eating cacti through the use of hardened papillae guiding the spines down the throat vertically).
Gomes, V.G.N., Koroiva, R. and Araujo, A.C., 2016. Vertebrate florivory on the short-columnar cactus Echinopsis rhodotricha K. Schum. in the Brazilian Chaco. Plant Ecology, 217(12), pp.1481-1487.
Peco, B., Borghi, C.E., Malo, J.E., Acebes, P., Almirón, M. and Campos, C.M., 2011. Effects of bark damage by feral herbivores on columnar cactus Echinopsis (= Trichocereus) terscheckii reproductive output. Journal of arid environments, 75(11), pp.981-985.