The answer is no. The Sonata for Two Pianos in D major, K. was composed for two pianos.

It dates as far back as the 18th century, ex. Mozart's Rondo in A Minor for piano, K 511 (1787).

At the beginning of the episode, he's playing a part of:

Franz Schubert's Piano Sonata No. 20 in A Major, D. 959, IV. Rondo. Allegretto.

Later in the episode, he plays a duet with Roz which is:

Mozart's Concerto No. 21.

The rondo form introduced in classical period is not to be confused with the renaissance rondo. It is also known as ABACADA form. The principal theme 'A' restates after each episode (B C and D as here). A popular example is Mozart's Marcia alla Turka from his piano sonata, K 331.