If you're looking for a project to demonstrate your ability to do the work for a living, don't write a game. Not that a game won't demonstrate useful coding skills, but the bigger skill you want to demonstrate is that you are able to solve problems. A game is a self-directed problem. You have not demonstrated that you can take someone else's requirements, communicate with them, and solve their problem. You haven't shown that you can work with or for other people.
Unless the game is for someone else, but then it still looks like you have to be entertained to be motivated.