In the credits, the Emperor Waltz, Op. 437, is credited to "R. Strauss" (presumably Richard). It was actually written by Johann Strauss, Jr. (no relation).
Not only does the dancing lesson depict Johann Strauss, Jr., playing a waltz he would not compose for another 35 years, but the version he plays is the "Emperor Waltz Paraphrase," a virtuoso showpiece for piano by Alfred Grünfeld (1852-1924), which was not published until two years after the latter's death.
Johann Strauss ll plays a waltz for the couple that he "wrote for the dance" after the wedding ceremony, which happened in 1854. He then proceeds to play the Emperor Waltz (Kaiser-Walzer) on the piano which he did not write until 1889.