My view of the whole system is:

The Horn is conical, defined by the 3 intersecting walls (a pyramid with an isosceles triangle as base).

[As a conical horn, it is a cone with about 83deg apex angle assuming spherical waves, or, about 104deg assuming plane waves.]

Our box is emitting waves at some distance from the apex, so it needs to have an emitting surface matching the surface of the conical Horn at that distance. We may consider that the box is functioning also as horn adapter, coupling the small driver’s surface to the large conical Horn surface (at that distance).

Obviously, there is nothing suggesting dipole operation. (In fact, I am unable to believe that a dipole in a corner would emit anything re bass).

As conical horns don’t have a (well defined) cut off frequency, the low frequency response is defined by the box:

Since we are using the driver’s front and back radiation to feed the Horn, we need to mess around with back radiation’s phase to avoid cancelation. (This is where the bass reflex theory is helpful for tuning the box and adopting it to the Horn).

Furthermore, this corner horn is functioning at a very limited frequency range: The box’s volume acts as a low-pass filter, permitting through the 2 ducts only low frequencies (depending on box tuning). At the box’s tuning frequency, the driver is not emitting anything, only the 2 ducts are operational. (Witch I think is a good thing)

Yes, this horn it is a different animal. For sure it uses the room better than conventional front horns do.