I really doubt it's so common that he doesn't skip a beat while sweet talking some girl. No reaction whatsoever.
I wonder if he had earphones on at the time which made it difficult to hear the shots?
It would seem that the person who recorded this was video-conferencing ("cam-chatting") with a female when this occurred, possibly using a program like Skype. At the same time he was probably running another program to capture a recording of of video session so he could play it back for his enjoyment at a later time.
I wonder if the recording was able to capture the first gunshot that occurred inside the police SUV during the struggle for the gun. It doesn't seem like he had just started recording when we hear the gun shots ring out. Perhaps the earlier shot was captured but it was overlayed with embarrassing "cam-chat" so it is not being played for the public.