If you're curious, here is the original, sung by Rimi Natsukawa.
She is a famous Okinawan singer who I absolutely love. It is one of my many regrets not picking up one of her albums while I lived in Japan. If you're curious about her stuff, which is largely more traditional than Nadasousou, I went to the trouble of making you a short playlist of my favorites here.
This is MONGOL800's cover of the song, and as you can tell, they changed it pretty significantly.
Who are The Majestics that MONGOL800 are playing with? I have yet to find out. All I know is that I'm relatively sure it's not these guys.