Gansett is an old beer company, and since its most recent incarnation in 2005, it's been pitching itself directly to the hipster crowd by pumping out vintage iconography- just a cursory look at the website will turn up a dozen examples. It's also a very sugary brew, which makes it an easy first beer for college kids experimenting with alcohol for the first time. (Last Sunday, I went for a drink with my sister and she dropped a shot of Amaretto into a glass of Gansett: Instant Dr. Pepper.)
Gansetts has also done an amazing job of marketing itself as the face of the Ocean State. Ad a born and bred Rhode Islander, I remember thinking in 2005 when the "Hi, Neighbor" signs went up, "Wait, what is this and since when has it been a part of my identity?"; now when I leave the state I make sure to bring a few Gansetts with me to remind me of home. And anyone who has lived in Rhode Island, even for a little while, can recognize how powerful a combination that Del's and Gansett shandy is. The first month it hit shelves, it was sold out at every liquor store near me within a day or two of being stocked. It tastes okay, but the sense of cultural identity, that you're enjoying something that is so intrinsically tied to being a Rhode Islander, is what really sells it.
e: Its also worth pointing out that Gansett's brewing is done by Genesee.