Perhaps Keith Jarrett's movements were a bit exagerated, expressing feelings while preforming is not so much a requirement as it is unavoidable for a human being to express some emotion.  Myself I play a few pieces on the piano and my mood will reflect in the way I play as will as the basic mood and tone of the piece.  The only difficulty I can see with movement is if it interferes with the actual preformance, I am reminded of the violinist on Celtic Woman, the way she moves sometimes it amazes me that she can hit any notes, let alone play so well, but that movement is part of her expressiveness of emotion.  I have heard the term 'Quiet Hands' in reference to piano instruction it may be possable that this would also translate to the whole body in remaining as still and quiet as possible. 

http://www.pianofundamentals.com/book/en/1.III.6.12.2

This is probably the "Glenn Gould syndrome" a sort of swelling of the ego, which affects some performers. But in the case of Gould, gestures and facial expressions are always meaningful in relation to music, whereas here it seems to me that there is a discrepancy between the exaggerated gestures of the pianist, and the simplicity of this music. This product, in my opinion, an effect a bit ridiculous (but this may be the goal, I'm not a  fan of Keith Jarrett, my opinion is totally subjective).
 In burlesque, however, I prefer  largely the famous sequence from the film Limelight, in which Chaplin plays the violin, accompanied by Buster Keaton at the piano: it's absolutely hilarious, but it's also very moving.
 Keith Jarrett still has progress to make...

This all has reminded me of 'Alice in Wonderland' and 'Through the Looking Glass'.  I believe in the latter there was a reference to the 'Anglo Saxon' messanger making 'Anglo Saxon' gestures.  Apparently they were a bit exagerated, and Lewis Carol was making fun of certain prominent people of his time.