Short version: He's not one of the greatest "contemporary" artists of all time. Not only does this expression not make any sense but Kanye West is also just not all that special.
Long version: I'm a musician. My strength as a musician is music theory. One thing that I can tell you is that people that we have recognized as "one of the greatest _s of all time" within music generally have an identifiable and visible characteristic to their writing that makes them deserve that title. When we look at the works of Bach, for example (an artist who was legitimately unappreciated in his own time), it is easy to identify why we call him a genius and why others call him a genius because he handles counterpoint with such ease; even if you don't listen to the music you can comprehend his genius by analyzing the logic and flow of his lines. A musician with even a basic theoretical background will be able to at least recognize the genius at work when Bach is composing.
One needs to only glance at a Coltrane solo to see why he is recognized as one of the greats.
Your example of Beethoven is a bit harder for someone who is not used to analyzing music to understand and it is not as apparent as, say, the genius of Bach, who wrote dense counterpoint and managed consonance expertly. But Beethoven gets recognition today for his role as a transition point between Classical and Romantic music and for personally doing much to differentiate the two and define the Romantic canon. There is also much to be said about the influence that he had on his fellow composers, both during his life and after it. People in the habit of analyzing music rarely dispute that Beethoven was a seminal figure in the history of Western music.
Bach, Beethoven and Coltrane all have in common that the music they write is challenging to take in. They tend to provide a lot of information in their music, even if there's not a lot of notes; they are explicitly recognized as geniuses because there is much depth to their choices and to their creative devices. Coltrane, certainly known best for his maximalist approach to improvising, displayed his genius perhaps most famously in a piece that consists almost entirely of half notes, a piece that is definitely not challenging to enjoy but certainly challenging to understand, particularly on the level that he understood it.
When I listen to Kanye West (an exercise I will freely acknowledge I have only engaged in due to the frequency with which people claim he's a genius) I can tell you everything that's happening in the piece on my first or second time through. He writes very straightforward chord progressions and over those chord progressions he writes melodies that conform to these chord progressions in a very straightforward way. He uses suspensions sparingly and resolves them when he does. You'll never hear him sing a passing note and he's very careful to avoid minor ninths; in fact, he seems to get trapped in pentatonics sometimes due to this (very typical) aversion to minor ninths and I applaud him when, on "Heartless", he indicates that he does know about the b6 and uses it liberally. We have reached a point in music where it is more or less impossible to be recognized as having an excellent sense of rhythm when you only operate within the confines of 4/4, which Kanye seems to be doing. He utilizes displacement and syncopation and that gives his lines a good rhythmic flow, but there are a great number of people capable of writing lines in 4/4 that utilize displacement and syncopation to create a good rhythmic flow. In fact, there are a great number of people who can improvise doing so on the spot; that ability might be described as the bare minimum requirement to play jazz, and if that's all you did, people might accuse you of sounding too much like a big band musician from the 1920s.
It is often said by his proponents that Kanye West will be seen as influential, perhaps specifically amending "after he's dead" to this. What influence will this be? The music that he creates is not innovative and I feel that that is not a particularly bold statement to make; people have been writing convincing 4/4 lines over simple chord progressions for a very long time now and it is very difficult to convince anyone thinking critically and historically about this that he's doing so in a virtuous manner. I could be wrong and maybe I'm listening to the wrong stuff. If this is the case, please provide me with recommendations and I will listen to them -- his back catalog is too large for me to listen to the entire thing, particularly since I don't really like him. But I don't think I'm wrong.
I will say, however, that he's a pretty effective producer and his style fits the current pop lexicon to a t.
