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Not sure if you've given up on this, It looks like you have the monitor connected to the port the AT commands are coming out of. The code is written to send the ESP commands to the hardware serial port and the monitor should be on the software serial port.You need your USB adaptor on the hardware serial port to download the sketch, but you then need the ESP on the hardware com port to get anything faster than 9600 working, so you will have to switch if you are developing.In my application, I put the ESP on the software serial port and switch it to 9600 straight away. The arduino can send at 115200 on the software serial port to change the baud rate, but can't receive at that speed.
Have you got the ESP connected to the hardware serial port? It looks like it is sending the commands to your monitor instead of the ESP. The code sends the commands to the hardware serial port, and if you have your USB adaptor on this it will not work. You will need your USB adaptor on the hardware serial to download the sketch, then swap the ESP to the hardware monitor, and your USB adaptor to pins 10 and 11 to monitor it.