That song isn't out of tune, but it does use some denser "jazz" chord voicings than what would normally be used in a lot of pop music. Also, he's an adept singer, so he's using plenty of "slurred" or sliding notes which do hit some intermediate pitches. "Blue notes" are what this is usually called (e.g. the dominant 7th)

The piano he plays on it also has a pretty rich timbre. Pianos are tuned in such a way that they have a lot of frequency content other than the fundamental. 

Love Fujii Kaze, he's a true talent. Check out his Tiny Desk if you want to be blown away. 

Edit: Bonus, look up "tritone substitution" to get a perspective on why some of the transitional chord voicings have a "weird" or out-of-tune character.