As a rule "dry" means more alcohol and less water, which in wine means a wine that is not sweet because more of the sugar has been turned to alcohol. As a rule, expensive wines (Chateau de Rothschild) are more expensive than sweet wines (Mogan David, Manischevitz, Thunderbird).
180 proof Rum is rather dangerous to drink without adding something wet, and generally feels unpleasant in the mouth. At least MY mouth, perhaps not everyone's.
I have not heard of dry beer or a dry beer process, but I am not an expert, and it is likely someone has bragged of a dry beer process. Special processes are the usual way brewers get people to pay extra for something that is probably not all that special.
The "Dry Movement" is a campaign to cause people to unite around a product.
Dr Pepper did something similar when they showed a lot of young people dressed like Mork from Ork in the famous "I'm a Pepper" Campaign. More adman hoakum.
I went to a rum factory where they told us that the bought the alcohol in bulk from the US, mixed it with purified water, and put it in barrels formerly used for Bourbon Whiskey. The usual industrial process for making alcohol does not involve fermenting sugar cane juice, but burning natural gas in a controlled atmosphere and then refining out the impurities. NOT a romantic process, nor one that anyone can claim was a family secret passed down through generations from Colonial times.