On things that might give calling somebody a genius is that they don't only perform well, they also bring something completely new.
As of instrumentalist virtuosos like Van Halen and Hendrix they both did that. I have no problem calling them musical geniuses in their field.
I saw a show with Van Halen where he explained how he saw Jimmy Page do trills with one hand on strings and one hand in the air - big deal he felt. Why didn't he do that up the fretboard while tapping with right hand on the right spots - and something new appeared. That many guitarists copied from him. And doing this combined with whammy/tremolo bar ripping even new dimensions into his performance.
- so this is something you can do on guitar
that is genius to me.
Same with Jimi Hendrix, he brought things that nobody knew a guitar could be used for. And I'm not thinking of spectacular things like burning it or something, I mean what he brought out. Just a trio but he sounded like a full orchestra. Like Machine Gun you can virtually see the battlefield and what is going on and bombs falling and machine guns blastering all over.
Sinatra was a genius in his field too. Both his quality of voice, and timing and everything.
You don't have to be a composer, conductor and performer to be a genius. You don't need to know all about how to write score either, just perform and have somebody transcribe that.
For guitar there are what is called tabs - that superseed what score can express. The actuall notes on which string and in which order. You can transcribe a performance on guitar much easier than with score. You mark bends, vibratos, and hammer ons and pull offs - which is very much part of how it sounds - since strings overlap in pitches and the particular string is used to get that sound. And very quick to learn how to read this - since very much hands on. So have to go to guitar and violin and this kind of instruments to get this kind of expression.
You cannot do many of these things on piano - so does that mean no piano player is a genius?
- of course not.
And Albert Einstein was a genius in his field.
Those are examples where I feel "genius" fit right in.