No, there's no longer a duty-free shop at the arrival area of the international airport.
In any case, for local rum it doesn't make any difference whether you buy it at the duty -free shop or not. It's about the same price, and sometimes cheaper, at local groceries. Figure US$5 to $10 a bottle, depending on where you buy it and the brand. A lot of people like One Barrel. I've always been partial to Duurley's gold.