If you don't want to watch the entire thing, here is their list:
10. Jean-Eugene Robert-Houdin 9. Lance Burton 8. Dante 7. Criss Angel 6. Harry Blackstone Sr. 5. Siegfried & Roy 4. David Blaine 3. Penn & Teller 2. David Copperfield 1. Harry Houdini
It's hard to tell whether or not this is a "good" list. Mostly, because it's not entirely clear what "good" means in this context. "Greatest magicians" is a fairly vague and also a fairly subjective term. Trying to decide what makes a great magician is up to the individual, like trying to decide what makes for a "tasty" ice cream flavour.
In this case, it's not really possible to criticize the list, since they haven't divulged their criteria for what makes a great magician. Without knowing that, it's impossible to say they're right or wrong. And what would end up happening isn't that we would be arguing over who was a better magician, but instead what was a better metric for judging the greatness of a magicians.
The world's tallest mountain
If I asked most people what they thought the world's tallest mountain is, the reply would come back "Everest". (Which apparently is supposed to be pronounced EE-verest since it's named after a person... go figure.) But the correct answer is not Everest... (!) The right answer is:
What do you mean by tallest?
Because if you're looking for distance from the "surface" of the earth, you get one peak. If you're looking for distance from the "centre" of the earth, you get a different number (because the earth spins on its axis, it's not perfectly round, it bulges around the equator. So a point at sea level on the equator is further from the centre of the earth than a point at sea level at the North Pole by multiple kilometres — more than enough to matter in questions like this.
And what do you mean by Mountain?
Most importantly, what do you consider to be the bottom of the mountain. Because where you start counting is also important in reckoning tallest. Everest is part of a mountain range which is already pretty tall to begin with. So it would be like a six year old claiming he's now taller than you because he's standing on a chair. It's also an open question as to whether or not you want to consider mountain-shaped things which lie under water. There are several volcanic island (think Hawaii) which start at the bottom of the ocean and poke up to the surface of the earth. They're incredibly tall (taller than Everest) yet most of their mass is invisible below the surface of the water.
None of this is a criticism, just really an observation. It's not like we hold click-bait to Olympic caliber standards of judging. This is just for fun. But what I like to try to do, as a miniature exercise for myself in empathy, is to try and slip inside the head of the list maker and try to see if I can reverse-engineer their criteria, to see if I can recreate their process based on their results. This is a kind of Bayesian exercise that challenges me to explore, compare and contrast different possibilities.
It could be that there are objective criteria behind it. Something like gross ticket sales, number of TV appearances, number of followers on twitter, shoe size. Or it could be that the criteria are entirely subjective; they picked the magicians they liked the best, or personally found most entertaining. Or it could be some combination.
There are two names which stand out on the list. The first is Criss Angel, since it's odd to see him on any kind of top-anything list since his work does not carry much respect from the magic community. He's certainly a celebrity by any stretch of the definition. Although it's more akin to Honey Boo Boo celebrity than Whitney Houston celebrity.
The other name which stands out is Houdini. The fact that Houdini is remembered as a magician seems to be a strange accident of history. He was certainly one of the great celebrities of his time and he had a multi-faceted career which included some magic shows, escape acts, film and even aviation. But the source of his fame and name recognition came from his escapes and escapes are, at best, at the periphery of magic.
It's these two names which lead me to believe that this is a "lamppost" list. The story goes...
You walk down the street to discover a man walking back and forth beneath a lamppost, staring at the ground, clearly drunk. After watching his movements for a minute or two, you decide to ask him what he's doing. He replies, "Looking for my keys."
"Where did you drop them?" you reply.
"Over on the other side of the street."
"So why are you looking over here?"
"Because this is where the light is."
This is the Lamppost phenomenon. It's also been described in Thinking Fast and Slow as the Availability Heuristic or WYSIATI (What You See Is All There Is). I saw Leonard Susskind describe "Lamppost physics" in a lecture. They were working in a particularly domain of interest, not because they were convinced that this was that this was the underlying theory of how the universe operates, but because it was the only area where the mathematics was currently tractable.
By knowing a bit about the landscape of magical talent, it's clearly this is a Lamppost List. These magicians aren't on this list because they are the greatest magicians. Although it's hard to say that anyone on this list was a "bad" magician, and I have a tremendous amount of respect for most of them, what's actually happening here is that are looking at a list of good magicians, who happen to be top of mind. Really this is a measure of "most famous magician" or "magician with the most hits on Google" rather than best magician.
Something similar happened earlier this year when BlogTO produced a list of the top five magicians in Toronto. The list itself was laughable. Again, I don't have anything of the people on this list personally, but when you look at the list as a whole, it's clear that no one is doing any kind of in depth research, looking for "the best" magicians. They're casually looking around, creating a list of magicians, then ranking those. The list could have been "The five magicians who showed up on my Facebook feed". What they see is all there is.