It's called "Satumaa Tango" and it's basically just an old and very, very popular song here. Every Finn probably knows at least the first verse* if you'd ask them about it. The composer is Unto Mononen, try googling for for tabs and stuff...
*By the way, he sings a mock version of the song in that video, so the lyrics are quite different The joke is completely lost in translation, because the verses don't rhyme in English. Anyhow, here's what Kekkonen is singing (this was actually half-impossible to translate):
Aavan meren tuolla puolen jossakin on maa Somewhere over the high seas there is a land Jossa sentään rauhassa saa kusta lorottaa Where one can at least take a piss in peace Joskus sinne ehkä pääse siellä nussitaan Maybe I'll get there sometime / they're getting laid there Siellä ehkä jospa jotain niin siinäpähän sitten oon There maybe perhaps something so then there I'll just be
(the last line doesn't make any sense in any language )