Scrabble was recently released on the Xbox One (part of the Hasbro Game Channel collection of games) and the game doesn’t exactly make it easy to figure out how to use more than one controller locally. When you’re setting up a game you can select whether you want AI or human players (up to four total), but by default it’s set to ‘share controller’ and there’s no way to change it.
In order for each player to use their own controller they first have to sign into an Xbox account. Once the player signs into a profile it’ll change from ‘share controller’ to ‘individual controllers’ and each player will be able to play the game using their own controller.
Hope this helps!