I am not a Sony fanboy, although I own a Sony A7riii. This video does seem questionable as it does not identify where the Sony mount came from and the red dot on it indicates that it didn't come from any recent model which have white dots. I also have used my Sony A7riii with long and heavy lenses and never noticed any flex at the mount carrying them around, shooting them, or even trying to flex them by hand with moderate force. The original A7 and A7r models did have flex issues, but this was addressed in later models. I have plenty of critiques about the A7riii (confusing menus, no in-camera processing, no in-camera filters for monochrome mode, iffy weather-sealing), but the body feels tight and solid.
This leads me to conclude that the video is a clickbait screed and best ignored.