I still have the same problem even if there is no noise going on in the background of the recorded video. I read somewhere it may have something to do with receiving/sending data so I disabled Wifi and put my phone into airplane mode and there is still a popping/clicking sound when playing back recorded video on all apps (LG G4 camera app, instagram, snapchat, google open camera, etc).
This is my second LG G4 because I lost my first phone while I was overseas earlier this year, BUT my first phone also had similar audio problems. So I'm guessing it's a hardware defect from early production models. It's probably not even worth turning this in to be replaced if I'm going to be getting the same model version in return. I plan to upgrade in the coming months to an LG V20 anyway. Actually, maybe I will wait a little bit longer before upgrading and get a later version of the LG V20 to avoid a similar happenstance that I've experienced all this year.