He says "For me falling asleep takes a cooling down period where my mind slowly disengages. That’s why watching old TV shows is so effective; it gives me something to focus on without letting me really engage."
You can get the same effect by listening to an audiobook, without having to worry about the glow of a screen at all. I use a cheap dollar-store speaker tucked under my pillow, where the muffled drone of the book is still distinct and listenable, but just soporific enough to lull me to sleep. The only thing to remember is to set a timer so it turns off, rather then continuing on for hours and potentially waking you up again.