Genre of Diablo 1's OST and music of a similar kind?
In short, his music is "Classical Instrumental". It can also be categorized as "Classical Video game Soundtracks". Overall, you would probably be best suited to checking out the Classical Genre.
Here are some recommendations to check out.
Personally I like Adagio for Strings and it has even been sampled for dance music. https://www.youtube.com/watch?v=izQsgE0L450
Update: based on your comment. What you are looking for is, Dark Ambient Classical music genre.
(2 Hours of Dark Music by Adrian von Ziegler) Example: https://www.youtube.com/watch?v=mIrt5MkGpy0
Mars by Gustav Holst, Night on Bald Mountain by Mussorgsky, Adagio for Strings by Samuel Barber, and any of the four seasons by Vivaldi. If you want to try videogame music, try The Ballad of Sir Kibbles by Suzemebachi, My Glourious [sic] Days or browse OCremix for remixes of video games you like (try sonic).