The video is signed by a diving center on the northern point of Sardinia. i.e. in the Mediterranean.
It's definitely some kind of anglerfish, but doesn't look exactly like the one that caught the diver in the other video (that video is taken in Norway, BTW). The colors are a little off, and the dorsal fin looks different from that of the monkfish we have in our waters. Yes, they're delicious, and no, don't stuff your hand into its mouth. It has a lot of teeth which are needle-like and all pointing inwards, so if your hand gets stuck, you'll have a bit of a job getting loose (ref. the unlucky/ignorant Slavic guy). When we spear them, we like to cut the lower jaw half off, severing one of the jaw joints completely to ensure against sticky situations like that. That's after we've killed them and gotten them off the spear, of course. And they're really delicious. I prefer to grill or pan-fry them. The meat is firm with a lobster-like taste and goes extremely well with a white wine and cream sauce. The offal doesn't just smell like for fish in general, it stinks. So you want to gut and clean it as quickly as practically possible to ensure the best quality of your food.
The North Atlantic monkfish can become as big as a man, so even if they're rather docile before you spear them, you can get quite a fight. They're also experts in camouflage, so spotting them as they lie on the bottom waiting for their prey isn't easy. The preferred tool is a pole spear and/or a suitable knife (i.e. not the GUE-approved mini knife...). I use two knives, my son uses a pole spear and a knife.