Sometimes called by the incipit "Коробушка" (Korobushka), this folk song (romanized "Korobeiniki") dates from the 1860s, though most people know of it from its use as the "Tetris A Theme" nearly 130 years later.
Here, Tom reads a simple lead sheet (just the melody line with the chord names written on top) and embellishes it into different styles, including changing the rhythm to 3/4 and 5/4.
The lead sheet Tom is reading from can be downloaded here: www.rmda.us/music.htm
Of course, you game fans may notice that the version in Tetris was in A minor, so this performance may sound flat to you as the lead sheet is in G minor (which is how Tom "runs out of keyboard" at the end since the lowest note on a standard piano is an A, so he can't hit that low G he wants).
The lyrics of the song are quite suggestive, about a peddler trying to peddle his wares to a girl who is not willing to pay the price at first. At least, that's what they mean at face value, but the implication of what the "wares" are and the "price" he wants her to pay is quite evident.
Anyway, sorry about laughing so much during the video. I hate doing that, but just couldn't help it!