Because that is how the Canon 6D is designed to operate in movie mode. The camera can capture a still frame while set to movie shooting, but external Speedlites/flash units are disabled for that function. Canon states this in the 6D manual: when shooting still photos during movie mode, an external Speedlite will not fire.

So this is not necessarily a fault with your Yongnuo flash, and it is different from regular Live View still shooting. If you need flash and full exposure control for a still image, you must switch out of movie mode and shoot in normal still-photo mode first.