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You watched the video already, right? Ok. The song at the end is the classic Yiddish show tune, "Romania, Romania" which has been recorded by just about everyone. The song was written by Aaron Lebedeff and was first recorded in 1925. I'm not sure who's version is used in the video (any guesses anyone?), but you can hear Aaron Lebedeff sing it at Amazon.
Update: Richard Kamins, of the N'Shoma radio show in Connecticut, thinks the recording is Aaron Lebedeff's version with the Shalom Secunda Orchestra from the 1991 compilation titled "Shalom-Music of the Jewish People", released on Fanfare/Pro Arte Digital. Thanks Richard!
Hat tip to Susan for point me to this one. Thanks!