Linkwitz Labs specialized in a lot of Open Baffle designs. I'm not cool enough yet to really understand what is going on with the photo I posted, but I have seen other similar concepts as well... So much depends on what's going on with the tube and whether it is ported or sealed. As far as I can tell, the direction of the driver doesn't really matter as long as it is connected properly for the driver's motor to move in-phase with the program being presented by any other drivers.
Take the Bayz example... if that tube is open all the way through it could be a push-pull or isobaric configuration, otherwise if the tubes are closed at the junction point, then it is just a type of resonant tube that may or may not coincide with a 1/4-wave tuning similar to a MLTL. The Tweeter Assembly in that speaker is clever in that it clearly supports the weight of the upper tube as well as being the tweeter housing.
For the drawing, it's almost a reverse Transmission Line with a Coupling Chamber a la Augspurger, except the driver and port would be reversed. Hard to describe that as a horn, but with the driver at the end and an expanding path for the backwave... You got me on a descriptor: it doesn't quite line up with anything I know/have seen.
If you want to read through the Linkwitz site, as I recall there is a bunch of design info there you may find interesting.
Otherwise, the only person I can think of that might have insight on OPs drawing is
@TLS Guy . Perhaps he can share his thoughts on that design.