The mystery Russian theme you posted is familiar to many of us due to Tchaikovsky using elements of it in many of his works, including the famous 1812 Overture. He borrowed the theme from the old Russian National anthem 'God Save the Tsar' written 50 years earlier.
You can hear different versions of the original music at a great website:
http://www.hymn.ru/index-en.html
Scroll down this website until you find the painting of the old Tsar where you will find a variety of MP3's (some of a similar quality to yours) to listen to.
I too have a CD and music of the Wynton variations on the Grand Russian theme, that also uses the old anthem.
Hope this helps.