I had a longer post planned about the director/choreographer Bob Fosse, but I haven't had a chance to finish it yet. But I did want to note that Fosse is an odd case of a great choreographer whose work often didn't contain much actual dancing, or at least, what was traditionally regarded as actual dancing. A lot of his most famous numbers, like "Big Spender" from Sweet Charity, are more about movement than dance; there are a few real dance moves but a lot of it is carefully choreographed and timed hand movements and foot stomps. And of course the trademark Fosse moves are a) snapping fingers and b) shuffling along while bent over backwards -- neither of which are exactly dance moves per se.
That doesn't mean that Fosse couldn't stage a great traditional dance number, because he could and did. But in some ways he resembles Busby Berkeley, who was not a great choreographer in the technical sense (actually he wasn't even a particularly good choreographer) but who was amazingly good at choreographing non-dance movements, both of the performers and the camera. Fosse's specialty was making sure that everything -- the dance steps, the non-dance movements, the lighting, the dance arrangements -- worked together to create the same effect; he was one of those choreographers who choreographed everybody, not just the dancers. That's why, more than any other stage choreographer, the numbers he choreographed are basically unstageable without more or less following the original movements (you can't do "Steam Heat" or "Big Spender" without the Fosse moves, because he made sure those moves were built into the music).
Here are two Fosse numbers to illustrate what I'm talking about; the "Big Spender" number from my favorite of his movie musicals, Sweet Charity (I'm not a fan of his version of Cabaret, while Charity is one of the better stage-to-screen adaptations of the '60s):
And while Fosse didn't directly work on the movie version of How To Succeed in Business Without Really Trying, it does more or re-create his stage choreography for "A Secretary is Not a Toy" (during rehearsals, Frank Loesser reportedly changed the song from a waltz -- still heard in the first refrain -- to its famous 12/8 metre to accommodate Fosse's staging ideas):