Hi there! I believe it was mostly done by hand, but using pattern repetition in a clever way. The artist probably made a couple of texture variations using straight lines and spread across the canvas by copying and pasting. Then he used that same frame and duplicated it, and dislocated it to another part of the canvas, selected a random part of this frame and rearranged it on the empty space, and so on for 24 frames. It isn't hard, however it's time consuming.
Because the rain is animated at 100ms, it flashes quickly so we don't notice the repetition, but it is there! It's one of the fundamentals of design and for animations like this I'd very much recommend its use.
I have two examples here, the frame #5 and frame #8, look how similar they are. I think they aren't exactly the same because this is an area of attention to the viewer, so the artist retouch it there specially after animating the whole texture.
You can save the gif and open on aseprite to look at it better.