If you're on the winners list, it's legitimate. They need your Social Security number so they can send you a 1099 next year. You have to pay income tax on your winnings.
Thompson and GE are separate companies. Thompson acquired the RCA trademark from General Electric. In addition, Thompson apparently has a licensing agreement with GE for the GE Consumer Electronics brand name.
But with all the companies that GE actually owns, and all of the licensing/branding agreements that GE has, it is an easy mistake.
Don't get me wrong, Thompson/RCA does make some pretty nice stuff. I was looking at the GE projection TV that Best Buy has on sale and thought it looked just as nice as some of the more expensive units. I hope that your prize -- no matter who made it or who's brand is on the box -- is a nice prize. Congrats!