Henry is the intern that worked at Treasure Island before Jake did. As explained in several logs from TGsEE, Henry wandered off without supervision, and Lisa and Greg could not find him. This later led to them hiring a new intern named Jake Smith.
The creator of the game, Matthew Phoenix Rodriguez, has stated that Henry would of made an appearance in the game. It is unknown yet of how he will appear, whether through a suit, a phone call, or even as himself.