If the RPM is steady at idle, then there's no problem. The computer is keeping the idle steady when the extra load of the AC compressor kicks in.
You must be holding the RPM at 2000 with your foot in the video. Is that right? If so, your FOOT needs to increase pressure to keep the RPM at 2000 when the extra load of the AC compressor kicks in.
Your foot is just not as clever as the computer, that's all. Steady foot pressure does not imply steady RPM always. It's just steady engine power, so the RPM can vary with the load.