Implementing AT commands with Arduino and ESP8266
You don't give a circuit diagram or very much detail about what you've done, but if I guess correctly...

You have flashed the code in your link to the ESP-01 (perhaps using the Arduino as a serial port adapter). That code is now running on the ESP itself - it's not running on the Arduino and controlling the ESP.

Flashing the ESP erases the stock firmware, so the ESP can no longer respond to AT commands.

I don't know of a way to reprogram the 'AT' firmware into the ESP but perhaps Google will help.

If I've guessed incorrectly, please explain exactly what you have done - with circuit diagram, setup steps and code.