Another great video-- how we can fix things ourselves very often if we try! I showed my wife this video because she also likes to fix things ourselves. And her favorite slogan is, "We're gonna need a longer screw."
I've also used superglue to repair broken plastic pieces like that. If it still doesn't seem strong enough with just the superglue, then you can use FastSteel Epoxy Putty to reinforce it. That combo doesn't work on all plastics, but it does work on most plastics. You can also use a soldering iron to melt the two pieces of plastic together. Works reasonably well but it cosmetically it looks horrible.
Great bit of work! I recently found out about superglue+cement, and thought this video was going to be one of those! Instead I found an entertaining guy running an interesting channel!