This is very impressive! and I can't think of anything else behind the LED, switch-cap interchange magic other than what my fellow readers have already mentioned...some trick in the sequencing logic.
The trick behind the lamps still glows with the battery removed might have been done using hidden supercaps?
The last one was a great fun and a great idea! Real demonstration of creative art using electronics!
Years ago, I was exhibiting in the COMDEX trade show. The booth opposite mine had a really impressive (for the time) portable computer. I don't recall exactly what it was. Maybe a tablet.
It was proudly displayed on a wooden cabinet protected by a plexiglass box over it.
Some years later, I read about that particular company in that particular show. It seems the reason they had the unit cover in plexiglass and sitting on a closed cabinet is because all we were seeing was the display. The guts of the portable were actually just a thick cable going to a hidden desktop computer inside the cabinet.
Maybe we're seeing a bit of that here.
Agreed, this looks like a case of a simple state machine and the presenter has memorized the sequence of the states.
The interesting thing about the no-battery demo was that the presenter only turned on one LED at a time. Whatever coincell battery was hidden probably couldn't handle two or more LEDs simultaneously.
Okay, that's impressive -- especially the part involving switching the switch caps.
I think it's probably done by a predetermined switch sequence that the presenter memorizes (say, blue/green/red/yellow, then green/blue/red/yellow), mixing it up to throw people off.
Power could be provided by a couple CR2032s hidden under the battery box. The lights look like LEDs hidden inside bayonet mountings to me; a battery and small SOT23-package PIC could be fit inside there to respond to switch commands.
However it was done, they did a very slick job...