This form factor isn’t actually new. This article is just about someone consolidating resources related to its current market options into simple documentation.
One major perk to this size is that it’s small enough that the vast majority of 3D printers can make plastic mounting brackets for it, making it a lot easier for people (who happen to have access to a 3D printer) to use small low-power gear that isn’t designed for rack mount.
So it’s most popular for people who want to run a few Pi systems, similar small SBCs, or mini PCs similar in size to a Mac Mini, or who want to throw network gear they already own that isn’t designed for racking into a rack. Even ITX systems don’t really seem like a great fit for this in my opinion, though it’s at least possible to fit them.
Rack width includes the rails/ears. That’s where the extra inch you’re referring to comes from. The actual size of equipment you can slide between the rails and inside the rack, not including ears, is about 17.75" for 19" racks and about 8.75" for 10" racks. That is indeed half the width. Or at least within 0.125", but I don’t know how accurate these numbers really are.
MicroATX very much cannot fit in this 10" rack.
Equipment that is “half-rack” or “half-width rackmount” tends to be primarily intended to mount two devices side by side on the same row of a 19" rack, but also can often be mounted in a 10" rack by attaching ears to both sides.