Unfortunaley I've tried that as well - different video players, also the sound is present when you playback any video directly on camera.
I also tried switching from mechanical shutter to electronic, same result. I have no idea what's causing this.
I'm having an issue with my X-T20 in video mode. Every video I've shot on it has this weird clicking noise in the background.
I've tried switching to manual focus and when I manually focus it makes other very similar noises so I guess it might be something to do with focus.
Lens used is Fuji 35mm F/2 R WR
https://www.youtube.com/watch?v=ZncxqdKVZyc&feature=youtu.be - video sample