That is not the takeaway I get from the paper. I read it as establishing that because testosterone levels has an well established impact on muscles growth, low

That is not the takeaway I get from the paper. I read it as establishing that because testosterone levels has an well established impact on muscles growth, low testosterone should thus impact respiratory muscles size at the point of getting the infection which in turn impact outcomes for people with respiratory disease. However this logic also imply that men should have an overall better outcome to respiratory disease than women, as men has on average more and larger muscles than women, but research into this tend to be more complex than that. Low testosterone has also been linked in research with increased inflammation response. One of the causes for deadly outcomes of Covid-19 is an over inflammatory response, thus the paper argue there could be a link between low testosterone levels and increase mortality for Covid-19 patients. The paper also mention a potential risk for people with high testosterone levels because a related gene which biological function of is unknown but which is connected to the function of prostate cancer cells. There seems to be indications that this gene can also modulate covid-19, and if we would inhibit the gene the theory is that it may reduce the effect of the virus. Clinic studies will have to show if it helps, do nothing or makes things worse, because right now its just a theory based on a gene which from my reading we don't know much about.