I still cringe when I hear the term, wrist snap, used. Coach Kyril uses the term but doesn't really explain what he means by it. The video was a bit dark and difficult to see but it really look like his "snap" was really more about forearm pronation than wrist flexion. He probably does use some wrist articulation but "wrist snap" would suggest something different than he is actually doing.
Now it's one thing to say "wrist snap" and then demonstrate what you actually mean by that directive. However, when someone else says, "Coach K says to snap the wrist" but doesn't actually show what is meant by this instruction, then the problems arise. This happens quite a bit -- and has been going on for decades. A coach will say "snap the wrist" on the serve or on the FH and then shows what he/she really means. But then the student will tell friends or others to "snap the wrist" and not properly demo the true/actual action.