You could try something like this. It doesn't give EXACTLY what you're looking for, but i'm sure after playing with some settings you could get somewhere close. This is as SHADER ONLY approach.
This is the setup I made:
What's basically going on here is that through a combo of a Mapping node, a Voronai Texture and a White Noise Texture , I generated a series of randomly gray-scaled vertical lines. I left in the Separate XYZ node even though I didn't use it because there is an option to only use the X coordinate if you want a more linear, less "noisy" look, but I think it looks better without, hence why I omitted it.
The key factor here is the Value node. Instead of using a number value, you can click on the field and input
#frame. This will cause it to use the current frame number as a value, meaning you can use it to constantly change the position, and "scroll" the lines.
On the bottom is a simple recipe for Cel Shading. I wanted to get a bit of a hand drawn for the shadows, I used it and multiplied it with the white noise texture, using it's inverse as a factor. This comes in handy, because it lets you mask different parts of the shadows if you switch the mix positions. See below:
"Normal" mix position gives this shader look:
Or, (and this might look better) you can reverse the positions on the Mix Shader like this:
And the shader result of this.
You can adjust the colorramp values to get a more true-to-image copy of the style you're trying to achieve, and you can also go one further by adding Freestyle to give black outlines. I'm sure by tweaking the randomness of the Voronai Texture_ as well as playing with the values on the Mapping Node, you can get something maybe close to what you like. Anything more would require hand drawing (grease pencil), I think.
I hope this helps some.