As the biggest selling instrumentalist of his generation,
Kenny G is certainly a crossover artist. Otherwise thousands of people who do
not care about jazz would not be buying his albums. However, this artist has
not diluted his sound to gain a mass audience. Though he does not play what
enthusiasts call classic jazz, his unique smooth sound is not at all commercialized.
It is pure smooth jazz.
Kenny G should be considered a crossover artists, because he did, in fact, crossover and do more than one genre of music. He started off as more blues, and at one point of his career you could describe as his style of music as R&B. He was definitely a crossover artist.
Kenny G plays the soprano saxophone, a jazz instrument that should define the type of music he is placed into. There is no way that he can be described as anything else because the instrument he plays is as such. He is a jazz musician because of the type of music he plays.
I personally think that Kenny G himself refers to his music as "smooth jazz", and it seems that most people would be willing to agree with that. There may be some audiophiles who would vie for a more obscure classification, but for the average consumer, it does not seem that there is any reason to question the genre that Kenny G has claimed for his music.
I think that this man did not cross over to any other genres, I think that he was simply a jazz musician, and that he did not want to be called any thing else but a jazz singer. He was one of the best smooth jazz artists in the world.