It looks like that permanent magnet it's hovering over is a simple dipole magnet, rather than an array. A diamagnet would be unstable in that position. Look at any video of floating graphite and you'll see it hovering on top of a 2x2 array of magnets.
Of course, you could fake it for a video by buying a special disc magnet with a multipolar magnetization pattern, but magnets like that are pretty hard to find.
If you already had a multipolar magnet for some reason, on the other hand, this wouldn't be too far fetched. You've got to think that with all the interest in this right now, the confluence of having access to a handy collection of peculiar magnets, knowing what to do with a bit of graphite, and being enough of a troll to publish a video, all in a single individual, isn't going to be that unlikely.
It looks (could be faked) like flux pinning is happening. Essentially, it's not moving but staying in place. Imagine trying to balance a magnet on another. It would not inherently stay in place.
Yes - Meissner effect is also called Flux Pinning. Superconductor will remain pinned to the magnet in any orientation. Diamagnet will only repel. The video shows horizontal hover - that confirms Meissner effect.
Flux Pinning is separate from the Meissner effect. Flux pinning only happens in Type II superconductors, where the Meissner effect of expelling external magnetic fields happens with both Type I and Type II superconductors.
https://www.youtube.com/watch?v=yeIizmhzPQc