Gorgeous homage to Fred Astaire and Ginger Rogers. Indeed, Glee is at its best when it is playing around with mashups and pastiche.
Here’s the original from the 1951 film Royal Wedding.
And here’s how they did it. Watch the above one first; you really appreciate how they filmed the dance and the amount of choreography, dance skills upon Astaire’s part, and set design skill that went into it.