You can't focus coldness. "Cold" radiation is simply less radiation. When you focus it, you get more radiation, not less of it. More radiation means more energy.
Instead you're simply seeing the effect of radiative cooling. See "Nocturnal ice making in Early India and Iran" [1]. By insulating the sides of a pan of water, and leaving the only window for radiation pointed to the night sky, you're ensuring that more radiation is leaving the water than entering it. Thus the water cools down.
So it would work equally with an insulated box with high walls. It's not about focusing the coldness.
[1] https://en.wikipedia.org/wiki/Radiative_cooling#Nocturnal_ic...
Yes, simply having an insulated container and having an opening pointing at the sky does work, but it's not the best you can do.
If you have an insulated box with tall sides, radiation from the object will reflect from the sides of the box back to it, keeping it warm (or less cold).
Screenshot: https://imgur.com/a/Oz4XEhy
This is the URL: http://solarcooking.org/radiant-fridge.htm
Pull the source and look at the last few lines. Alternately, hover your mouse over the area at the bottom of the page and look at the URLs it would go to if you click.
I've tried contacting the author but the email no longer works. I've not yet contacted the site owner.