This is great. It reminds me of the way arcades used to be, before everything was spaceships and guns. I say this without irony, knowing that my game prominently features both.
The graphics remind me of the family members in Robotron, so I was half expecting big fullscreen pixel-shatter animations. Actually, I think it could benefit from some of those, but then I think that about everything.
I liked the way the scoring system rewarded hitting more than one couple at a time with extra points. I would have liked to see more complexity there, to reward more interesting play.
It reminds me -- just a bit -- of a C64 game named Stars and Rings, which has a similar mechanic involving spinning an object and releasing it at the right moment. However, I don't recall seeing anything else remotely similar, and I love the mechanic, so full marks for innovation.
I was just slightly confused by the direction the partner took when I flung him. He headed 90 degrees clockwise relative to the direction I expected. I was expecting him to keep moving in the direction he was moving when released, if that makes sense. Instead, it behaves more like the main character pushes him directly away. I don't think this is a big problem. Actually it might even be easier to control as it is, but it was counter-intuitive to me at first.
The sounds are great and I wouldn't change anything that's there. However, given that it's a game about dancing it really ought to have some music.
Unlike the author and some of the other commenters, I think it's a clever and fitting use of the theme.
I had a lot of fun with this. I look forward to seeing an updated version with more different types of dancers. Please don't change it to an underwater theme. I love it as it is, and it would lose some of its charm.