so I toyed around a bit, I'd say this doesn't look quite as good, but it will scroll, I can explain a bit more if you want but I think it's easier to understand if you look yourself at it. I exposed some options, size controls the scale of the edge mask noise, and mapping is where you connect the mapping node to scroll, but if you want finer control go inside the group and tweak the ramps.
Sorry for jumping to conclusions earlier, I should have taken more time to test.
old post (this is wrong):
This is because this first noise texture node is only controlling the scale of your second noise, which is the one that is actually controlling the look of the texture the most.
The mapping node should be connected to the noise node right before the ramp node.