Ginger keeps up and, at times, challenges Fred in a call-response kind of dance. There is a sense of equal footing and feeling each other out in this scene.
Overall, I liked what Wes Gehring, Ph.D. said in the lecture video about the difficulty of genre classification. This movie is a carefully crafted comedy with music and dance and that would be the expectation because of the principle players of the film. By this time Fred Astaire is a full-blown star and enjoyed for both his dancing, singing and acting. Ginger Rogers is appearing in many other vehicles that show her as a triple-threat performer. Their relationship with viewers has been established since this is the fourth pairing. Add the music of Irving Berlin, and this movie fires on all cylinders.
(As an aside, I ask, did people really see movies in terms of classification at this time? Did studios market them with a particular category?)
Today we over classify everything to the point of alienating certain audiences from films because they get labelled a "chick flick", or romcom, or an action movie. Back in the 1930s, movies were entertainment and escape, especially because of the economic times, and something that entertained you was the name of the game. Top Hat fits the bill.
If we must classify this film, I would say it is a screwball comedy as it fits with the sparring couple concept that belongs to that genre. The screwball comedy pitted the male and female against each other, tending to show them as equals in the game. That is what I think of when I watch Fred & Ginger movies. The music and dancing progress the plot and romance and allow us to see the pair develop into a couple.