I suggest you activate the node wrangler addon (if you have not already). You can preview what each node is outputting by selecting it and hitting ctrl+shift. This will help you understand what is going on.
The basic idea is that when you separate the x, y , z vectors of your object and plug the z output into a colour ramp (or linear gradient) you get a black and white gradient from top to bottom (along its z axis).
With the node wrangler addon if you select the colour ramp and hit ctrl+shift you will see the gradient mapped to your world.
I used that gradient as a mask to mix the 2 background shaders and eliminate the copy of the image.
As you are using the objects coordinates to map your world settings when you rotate your empty the worlds z axis also rotates.
Yes it can be simplified the second mapping node was not necessary (I left it out in the second example.)
If you do this it does change a bit, If you look closely to your image you will see that the black parts will show the colour of the second background (the noise colour) and they will no longer be black.
I used the alpha output because the image does not have one!
The alpha output is giving you a white square ( well 2 of them there is one at the top and one at the bottom), where the image is, on a black background.
Once you darken the gradient mask with the alpha output you get a mask with only one white square where the image is.
The result of using the alpha output and darken node is that the black parts of your image stay black!
With a black background this is not needed but if you want a coloured background you will definitely see the difference.
Without the alpha:
Also note that as I left the top colour of the darken node at the default value (0.5 grey) the yellow background colour has been mixed with the black background and is darker.
With the alpha:
Yes putting the sliders closer together only makes the transition of the gradient more abrupt, I did this to make sure the edges of the image do not fade into the sky, It might not be necessary in this case.
I hope I have not confused you even more!