This one often surprises people the first time they see it. But it's been perfectly well understood since the work of Faraday and Lenz and a bunch of Frenchmen (Biot, Savart, Ampere etc) was tied together brilliantly and beautifully by James Clerk Maxwell in the 1860's showing, in the process, that light is in fact an electromagnetic wave and relating its speed to the properties of capacitors and inductors.
Your man in the video is a bit foggy about both the numbers and the detailed principles though.
First, copper is not 75% as good as silver. It's 94% as good.
Second, the physical dimensions of the pipe really matter. If the pipe has a narrow bore and/or a thick wall it will slow the magnet down more.
Third, cutting the pipe could have been very instructive, but only if he'd cut it in the right direction. As he says, the moving magnet generates a current in the metal. It's the current which generates an opposing magnetic field and slows the falling magnet down. But the current flows around the circumference of the pipe, not up and down it. So cutting the pipe into rings makes no real difference. If, however, he'd put one long cut down the length of the pipe to break the round-and-round current path then the current wouldn't have been able to flow and the magnet would have fallen just as if the pipe wasn't there. Something similar is done with the interwinding screen in the mains transformer in your amp - it's wound around the magnetic core but a small gap is left to stop any current flowing in it. This way it acts as an electrostatic screen but it doesn't disrupt the transformer's magnetic behaviour.
The logical conclusion of all this is to use a perfect conductor (a superconductor). The current flowing in one of those is large enough to stop the magnet falling altogether. In this video the black lump is not a superconductor at room temperature, so the magnet falls onto it. But when it's chilled with liquid nitrogen it becomes a superconductor and the magnet can't fall onto it.
If you're interested in taking this a bit* further then the sums are here http://www.msc.univ-paris-diderot.fr/~phyexp/uploads/LaimantParesseux/Tube-Aimant2.pdf.
*OK, the sums aren't quite trivial ...