Do I need to play the other Infamous games?

I know this game takes place several years after the last game, but do you think it'd be alright to jump into this one?

Yes, it will be alright. I listened to an interview with one of the developers(Chris) on IGN and he said that they made the game so that anyone can jump in without having ever touched another infamous game. He also said the control scheme will be different from the other games too. So you'll be fine.