I am trying to upload the sketch to a standalone ATMega328 chip, but I keep getting "programmer not responding".
Arduino IDE sees ATMega328 among serial ports though.
ATMega already has Arduino firmware obviously and it passes the LED blinking test..
describe all the connections you have made, we need more to go on.
GND - to ground
5v to Power
TX to pin 2 on ATMega328
RX to pin3 on ATMega328
there is also 16Mhz Crystal connected. Everything else is done like
You have no auto reset connection so you have to do a manual reset at just the right time to upload. Otherwise fit a 0.1uF from the reset pin to the DTR.