You can just make out small components in the so-called piece of wire. Just at the places he touches. I do recall something similar in Scientific American once using hidden diodes, and ac.
It's trickery but not video trickery. The circuit does work in real life but it is nothing like the simple series circuit on the diagram. There are many more components than you can actually see, and it's not a simple DC circuit. The main part of it is hidden in the battery connector, with some components hidden underneath the LEDs and covered with red resin, and some tiny ones attached to the wire at the points where he touches it.
Here is the solution to one of his earlier tricks
I imagine he'll post the solution to this one at some point.
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