I don't think the mystery is solved yet. "Voi che sapete" doesn't contain any of the music featured on the original audio clip you posted.
The titling of the tracks on this Rondo Veneziano album is pretty thoroughly awry. Everything that is listed as coming from an opera is actually from an instrumental piece, and vice versa. Track 2, for example, is entitled "Don Giovanni" but the music is from the 40th Symphony in G Minor. Track 4 is entitled "Eine kleine Nachtmusik" but the music is the overture to Marriage of Figaro
. Track 7, alleging to be from the Jupiter symphony, is the Queen of the Night's aria from Magic Flute
. And Track 9, alleging to be from Magic Flute
, is from "Eine kleine Nachtmusik."
The audio clip you're inquiring about sounds like a piano concerto, or possibly a chamber piece with piano. I've listened through a couple of Mozart piano concertos but have not come across the music yet. I'll let you know if I find it...