**IF** the switches are simple series SPNO switches as shown and   
 **IF** the LEDs are standard LEDs then by definition it is not possible - he is using video fakery and the demo is less than valueless. 

"Not possible" is able to be said with certainty because examining even SW1 + SW2 + SW3 in series current can flow only when all 3 are operated. 

HOWEVER if the "switches" and "LEDs" are modified then it is possible and it becomesa conjuring trick with rigged props. Still pretty pointless, but possible.

One of various ways:

 - Each switch contains a current determining circuit. 

 - Each LED contains a window comparator and current bypass circuitry

 - LED1  lights for I1 or (I1 + I2) or (I1 + I3) or (I1 + I2 + I3)

eg say I1 = 10 mA, I2 = 20 mA, I3 = 40 mA.

LED 1 will light at 10, 30, 50 and 70 MA
LED2 will light for 20, 30, 60, 70 mA
LED 3 will light for 40, 50, 60, 70 mA

So  
mA LEDS lit  
10 001  
20 010  
30 011  
40 100  
50 101  
60 110  
70 111  
 
Hopefully that table looks familiar. 

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There are many other trick ways and it is more likely that the system is "a trick".
.