This guy is talking about resilient channel while he is playing with another thing, a hollow box pointed out by red arrow. What is that?
That is a 4" deep Octagon Box.
It is a standard electrical junction box for mounting lights and other ceilingey things. (not a fan; that takes a reinforced box). Note the single Romex (NM-B) cable entering it.
The person is applying a junction box extension ring. They're modestly expensive, especially since, as an obscure item, the big-box stores will be wildly overpriced (for some reason, they do not specialize in big boxes). Regardless, it isn't necessary. A junction box that easy to remove could simply be removed and remounted with a spacer behind it. Use a slice of the very same stuff being used to thicken the ceiling; solved. (as it happens, drywall is a good firestop, which just goes to prove, nothing is completely useless). The excellence of the firestop helps the steel junction box do its job, which is to distribute arc heating so nothing reaches combustion temp.
Also the person is using a power tool to run down screws on electrical boxes. That's done for "coolness" or for TV-show pacing; or because "if all you have is a hammer" (the drywall screws need it). You shouldn't use power drivers on electrical boxes in real life, because if you cam out the screw or God help you, strip the screw hole - you'll regret it.