After a very brief attempt I can say that the aim seems to be to manipulate the direction of the Y-axis conveyor belts with the huge arrow button in order to couple up the girls. So you put Sayaka on a certain tile, next you can put Kyouko on top of her to get points. Putting another Sayaka on top will be bad. Not sure what the artist's "okay" pairings are, but it just mentions how many "Couples" you got on the score screen.
At the end I got a picture of Homura handing over some valentine chocolate. Don't know if it changes depending on who you scored more points with.
