Haven't seen the video yet, but I've been placing our box fan facing outward in the room adjoining our bedroom and opening a window beside the bed. It feels like it's blowing hot air out and sucking cold air in but I could be wrong.

EDIT: incredible!! I'd have never thought to move the fan away from the window but it makes so much sense. I wonder if it could be related to Bernoulli's Principle as well? I'll be giving this a shot tonight when the temperature drops again. I'm thinking I can set up our smaller fan back from the window and use the box fan to move air from one air of the house to the next.

I wonder if it could be related to Bernoulli’s Principle as well?

Possibly this and also because fan without tube causes a circular, or more precisely donough-shaped vortex: In the front of the spinning "disk", the pressure becomes higher , in the back lower, so air flows around the disk from high to low pressure.
The Bernoulli principle would lower pressure in the "jet" of air going out of the window, and suck in other surrounding air.

UPDATE: I gave it a shot with the smaller fan pulled back from the window about one and a half feet (I didn't have anything to rest it on to move it further back) and there was very little air movement. I tried with the box fan pulled back as well and it was the same. So for last night I just put the box fan back in the window because I was roasting XD

My apologies, I realized that somehow I clicked on this video, and instead was shown a video on Portable Air Conditioners of all things.