Facts established about this video so far:

Pianist: Dmitri Shostakovich (1906-1975)
Trumpeter: Leonid Yuriev (1913-1971)
Conductor: Maybe Aleksandr Gauk (1893-1963)
Orchestra: Probably Leningrad Philharmonic
Venue: Moscow Conservatory "Great Hall"
Date: Some time after 1933, October 15th, and, most likely, before the "official ban" of early 1936. So, 1934-1935.