Shows compilation error: ESP8266WiFi.h: No such file or directory while executing library file mqtt_8266.ino file
The ESP8266WiFi library is written specifically for the ESP8266. You can't use any code that is written for that library with any other board.
If you aren't directly programming an ESP8266 then you will either need to modify your sketch to not use ESP8266WiFi or else not use it.
If you are trying to directly program an ESP8266 then you won't be able to use the Arduino Web Editor because it doesn't support 3rd party boards. You'll need to use the real Arduino IDE instead. You can download the Arduino IDE from this page:
And then install support for the ESP8266 following these instructions: