I never fully got Eddie Van Halen. I guess he was the forerunner of all the speed players of the 80s, but I never really got the groove for that. For american whiteguy band guitar rock, I think Steve Perry writes better parts than Van Halen. But I don't like Aerosmith or Van Halen. Might as well go to the source and listen to the Stones if you want two guitar rock--
But to my mind the most influential "rock" guitarists would have to be: 1) Jimi Hendrix; 2) Clapton; 3) Jimmy Page; 4) maybe then Duane Allman (but only in combo with Dickie Betts); 5) Keith Richards (sharing his spot with Chuck Berry). To me, Chuck Berry has to be the beginning of rock guitar (maybe with a nod to bluesmen like Robert Johnson and B.B. King and Hubert Sumlin, etc.). Because Chuck pushed guitar to the front as a lead rock instrument rather than horns. Chuck is far more important to the development of rock than B.B. King, for crissakes, and just about everyone else. For that matter, Charlie Christian or Lonnie Johnson is more important than B.B. King.
I know the list is "greatest" but that term should include both influence as well as technical prowess. Hendrix has influenced a lot of players, but Chuck Berry almost singlehandedly (with Buddy Holly and the early Elvis) created a genre.
I hate these lists, but at least they get you thinking.
P.S. Neil Young probably deserves to be in the top ten for sheer idiosyncratic power and emotion of his electric and acoustic playing. "Cortez the Killer" is one of the few post-Hendrix songs to be in Hendrix's ballpark.