As far as I understand the privatized companies are monopolies-- these companies were formed from the JNR by geographic area served (hence "JR East", "JR West" etc.)
The bloomberg story is really light on details for why and how the privatization occurred; for a much more in-depth view, see S.Y. Lee's Substack, for example this post: https://seungylee14.substack.com/p/the-death-and-privatizati...
(An interesting fact is that most of JNR's debt at the time was retained by the government while the assets and revenue were privatized)