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

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.