> The pattern across any single frame is entirely random noise.
This is untrue in at least one sense. The patterning within the animated letters cycles. It is generated either by evaluating a periodic function or by reading from a file using a periodic offset.
You could do that, but that's not what the page is doing.
You don't even need to maintain the approach of having the pattern within the text move downwards over time. You could redraw it every frame with random data, as if it was television static. It would still be easy to read, as long as the background stayed fixed.