Class that only creates an instance of a new game
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();
    }
}