Class that only creates an instance of a new game I am creating a game. I am at the final phase for the underlying basis and I am wondering whether what I am doing is recommended- if it's convention. 

All this class does is create an instance of the game. That's it. The game instance takes care of the rest (i.e attaching the menu screen to the screenManager (i.e displaying the menu screen))

As a result, this class complains that we're not using the value. But that's exactly what we want, we HAVE no use of this result. I just want to know, is this OK?

    public final class RunGame
{
    private RunGame() {}

    public static void main(String[] args){
       Game game = new Game(); // We want to start a new instance of the game, but we have no use with the result!
    }
}
Being pedantic about the terminology: Not the class, but the IDE, complains about the unused value. As hinted by markspace, I agree that first creating an instance of the game and then starting it is the natural way to think about it. Don't add to many side effects to the constructor that the user might not expect.

To get rid of the warning about the unused value, don't assign the instance to a variable. Just do new Game() or new Game().start().

Here is my recommendation, with fixed formatting and changed class name (since RunGame sounds like a method name). I also removed the constructor from the main class; I don't think you need it, since main() is static.

public final class Main
{
    public static void main(String[] args) {
        new Game().start();
    }
}