Okay, this is less about materials and textures, more about the recently-exposed ability to animate movie textures in Eevee.
I have mimicked this node setup to no avail. They are using .MOV and .MKV, I am using .FLV, if that means anything. I learned it still does not animate when I hit the play button, but it animates when I scrub with the preview open, which fails when the preview is closed. I have given it a large amount of frames to work with, over 20000.
May I please ask if there is anything I am missing?