According to mediabiasfactcheck.org, Aspen is a moderately left-leaning think tank that is accredited to report "highly factual" See mediabiasfactcheck.org's report on Aspen here
Aspen's claim is not saying that drinking water prevents contraction of COVID-19, they are instead saying that sustained, ample water intake while sick can help your body respond to and recover from COVID-19. When ill, your body loses water at a more rapid rate than when you are healthy. Aspen references increased sweat due to fever, coughing, and losses due to vomiting or diarrhea.
This paper acts as a nutrition guide and gives tips on how best to stay hydrated and nourished while fighting off COVID-19.
You said that various social media posts are referencing this article. If these social media posts are extrapolating from this Aspen paper that "Drinking large amounts of water can help prevent COVID" then they are misinformed / formed an incorrect message from this paper. Aspen never claims that drinking water prevents COVID-19.
Rating: False. Aspen never claims that drinking water prevents COVID-19 contraction. Anyone who references this paper in means to support the opinion of "drinking water prevents COVID-19" is drawing an incorrect conclusion.