From the article: Commodore DOS has been in existence since the Commodore 2040 drive from 1978, and new firmware code for Commodore DOS devices is being developed to this day.
This design is clearly inspired by Mainframe I/O design, channel based with intelligent devices, with very little abstraction. It is very simple in that it deals with bytes, memory addresses, and the disk blocks/sectors.
It really is almost a naked I/O KERNAL (to be user friendly another layer of abstraction should have been built over it by the time the C64 came out and memory was cheap).
Still, super impressive what was crammed into the PET disk drives. For 1977 this is very sophisticated stuff. Apple's DOS was easier to use, but less flexible and bound closely to the disk hardware.
I can't comment on the third leg of the Trinity, having never examined TRS-80 DOS in any detail.