It's probably worth mentioning what "rock and roll" actually is. There are two definitions of "rock and roll".
The first definition is a genre popular of music that originated in the early to mid 1950s and ended in 1959, because of the following events:
- The drafting of Elvis into the army (1958)
- Little Richard retiring to become a preacher (1959)
- The arrest of Chuck Berry (1959)
- The scandal of Jerry Lee Lewis marrying his underage cousin (1958)
- The death of Buddy Holly, Ritchie Valens, and The Big Bopper in a plane crash (1959)
- The payola scandal that rocked (no pun intended) the music industry, taking down a number of well-known rock and roll DJs, including Alan Freed, with it (1959)
Under this definition, "rock music" is a genre of music that began with "rock and roll" and branched out in a number of different ways. This definition also implies that the vast majority of the artists in the Rock and Roll Hall Of Fame shouldn't be in there, because they're not, strictly speaking, "rock and roll". They're a different rock sub-genre, like metal or grunge or surf rock or punk.
The second definition has the same start date, but essentially doesn't end, and instead somehow becomes the same as the all-encompassing genre of "rock", spawning all the sub-genres. It should be noted that early 1960s rock sounds fairly different than the rock and roll that ended under the assumptions of the first definition, as surf rock, and soul, the two biggest subgenres to originate around that time.
With the two different definitions of rock and roll established, there are certainly other acts that aren't "rock and roll" or "rock" that are in the Rock and Roll Hall of Fame.
- Albert King
- Bobby "Blue" Bland
- Jimmy Reed
- John Lee Hooker
- Muddy Waters
- Bob Marley
- Jimmy Cliff
- Charlie Christian
- Miles Davis
- Bee Gees (they were soft rock in the early 70s, but it's safe to say their disco stuff got them in)
- Donna Summer
- Michael Jackson
And then there's the question of other genres, like Soul, Funk, Rhythm and blues, etc. Are these "rock and roll"? What about soft/folk rock, like Crosby, Stills, & Nash or The Byrds or James Taylor? Are they "rock and roll"?
What makes these artists and genres "rock and roll" but rap not? I don't think anything does, really. I think the Rock and Roll Hall of Fame is really more about popular music than "rock and roll" or "rock", per se; it just started with the 1950s rock and roll era and moved forward.
But we can also look toward the Rock Hall for more information. First, you have their article entitled "Planet Rock: Hip Hop is Rock and Roll". As further evidence, look towards the eligibility requirements for the Rock and Roll Hall of Fame:
To be eligible for induction as an artist (as a performer, composer, or musician) into the Rock and Roll Hall of Fame, the artist must have released a record, in the generally accepted sense of that phrase, at least 25 years prior to the year of induction; and have demonstrated unquestionable musical excellence.
We shall consider factors such as an artist's musical influence on other artists, length and depth of career and the body of work, innovation and superiority in style and technique, but musical excellence shall be the essential qualification of induction.
Note that there is no stipulation of genre. All influential artists who have demonstrated unquestionable musical excellence are considered. Also, looking at that page, you'll see
Ballots are then sent to an international voting body of more than 600 artists, historians and members of the music industry.
I think this is the most important insight. 600 people decide what "rock and roll" within the scope of the Rock and Roll Hall of Fame is. They have opened it up to fans to vote, but the top 5 artists by fan vote count for one ballot each. So, essentially, fan votes don't count, and 600 people choose what "music excellence" is and how "influential" and "innovative" an artist was.
This is why you have sub-genres that are seemingly left out of the Rock Hall, like progressive rock (as @JohnnyBones pointed out), electronic music, glam rock, art rock, and others. You also have countries left out, since almost every artist in the Rock Hall is from the U.S., the British Isles, Canada, or Australia; all English-speaking countries. And as you pointed out in your question, an executive decision was made to include the first rap artist, despite the fact that not enough of the 600 people were behind it. Whatever the 600 people say is "rock and roll" is rock and roll in terms of the Rock Hall.