Arduino UNO with integrated ESP2866 wifi not working correctly
You are obviously currently programming the ESP8266, not the Atmega328p. The board seems to have DIP switches on it. With those you can control, which chip is connected to which. The product description has the following table
Connection  DIP
1   2   3   4   5   6   7
ATmega328&lt;-&gt;ESP8266     ON  ON  OFF     OFF     OFF     OFF     OFF
USB &lt;-&gt;ATmega328    OFF     OFF     ON  ON  OFF     OFF     OFF
USB&lt;-&gt;ESP8266 (Update firmware or sketch)   OFF     OFF     OFF     OFF     ON  ON  ON
USB&lt;-&gt;ESP8266 (communication)   OFF     OFF     OFF     OFF     ON  ON  OFF
All independent     OFF     OFF     OFF     OFF

If you want to program the Atmega328p on it, you need set the DIP switches to the combination &quot;USB &lt;-&gt; Atmega328&quot;. Currently you most likely have the combination &quot;USB&lt;-&gt;ESP8266 (Update firmware or sketch)&quot;, which means, that the ESP is connected to the USB chip (and thus to the PC) for programming. For blinking the Arduinos buildin LED you need to program the Atmega328p.

About the blink sketch: In the tutorial video he programs the ESP. But in the blink example he changes the delay time to 5000, which would mean on and off times of 5s. The LED, that he is pointing to, is blinking much faster, though he doesn't address this. I think he actually has the standard blink sketch on the Atmega and only pretends (or just didn't notice) that this happened due tp his programming. As you don't see a blink with the ESP, but with the Atmega, I would guess, that the LED marked with L is connected only to the Atmega (like on a normal Uno) and the ESP doesn't have any LED to blink connected. So everything is actually working as expected, the tutorial was just bad at that point.