Please ask them to submit their system specs and provide videos please, couldn't see much from the three second clip you posted.
I have the same problem with flickering
CPU - AMD FX8350
GPU - Sapphire r9 280 3gb DDDR5. Driver Version - 17.6.2
OS - Windows 10 64bit
Power Supply - 650w
Ram - 8GB
Same thing happens when I minimize the game or open steam overlay while playing a game and have AMD relive on. It can be stream, video or relive, doesn't matter. After same actions, my mouse can start to be very smooth like I have vertical synchronization on, Input lag or something and after that, I need to stop streaming or capturing and end task from task manager to make my mouse movement normal again