"But he doesn't even sing!"
If music only consisted of lyrics, you'd have a point. But you already said exactly how the infringement happened: playing the guitar.
The content usage is clear: the video uses the song's melody, and therefore is infringing on copyright.
It doesn't matter how long or little is played. Copyright infringement suits have been successful when only seconds of the original work were copied, because that short section is important enough to require protection, and its use to deserve compensation (in the extreme, because it comprises the entire work).
While this video is on a commercial channel it's quite evident that guy did it for educational purposes.
If done for commercial purposes, this is almost surely the deciding factor over others in USA fair use, and clearly disallows UK fair dealing, and in most other jurisdictions would tend to make it disallowed usage as well.
Put more simply, you can't justify infringing copyright in the material used for teaching when you're getting paid for that teaching, any more than you can justify theft of real or tangible property on the same basis.