It removes (or tries to remove) the gain from the equation.
If you increase gain, you amplify the noise as well. So now you have more noise, and a different figure. So you'd need a curve for output noise vs. gain. It happens, this curve would be nearly a straight line. So you can just express input referred noise as a single number, and multiply it with your actual gain.
It's still expressed for a given gain (like G = 6 in your example), because they need to test it with some test circuit, and want to specify what they used. Furthermore, the output noise isn't perfectly accurately gain * input referred noise - so the curve we talked about earlier isn't exactly straight, and maybe doesn't start from 0. Which is why they still need to give a different figure for different gains, but at least they are closer to each other, and often they just get away with specifying one value.