Well, yeah, its not really bear. But doesn't it have an aging process? Like, I know that the brand Vernor's ages for about 3-4 years...in a barrel, even.
Lecture mode: Initiated!
Ginger beer was originally created by the temperance movement as an alternative to beer (root beer, flavored with sarsaparilla root, is a similar alternative). Originally, the carbonation in the drink came from a fermentation in the bottle, which could also add trace amounts of alcohol to the beverage.
Modern day beverages are carbonated through introduction of chemically produced carbon dioxide under pressure (most often, if you buy a soft drink that's carbonated by fermentation, it's most likely a microbrew and costs a mint), which evaporates when not under pressure.
Aging is a completely different process, which has nothing to do with alcohol, it merely means storing something for a time, which gives time for certain chemical reactions to form new flavor compounds through leaching from the container or interaction between the food, certain bacteria and chemicals in the air. Smoked and/or dried meats are commonly aged, as are several kinds of cheese.
Edit: Described wrong reaction. Sorry!
