I first encountered the “Antop” type antenna a few years ago. It was manufactured by the Qiaohua\Shenzen company and sold through different distributors under different brand names. The “Eaglestar” brand was the first I came across 6 years ago.
At that time it was a a “slotted waveguide” design used in cellphone tower antennas, More on this antenna type here:
http://www.antenna-theory.com/antennas/aperture/slottedWaveguide.php
Here is the Eaglestar inside:
The plate(s) are the receiving element(s).
Inside the Antop 400-BV:
The two 400-BV plates are the receiving elements: rectangular, flat figure-eight UHF dipoles. The total effective metallic antenna surface area is twice that of any flat, paper-thin antennas. If one measures the three lengths of the portruding sides, they come out to be 8 inches - the same as the Channel Master 4 and 8 bay antenna elements. This is the average UHF wavelength.
The added gain comes from the fact that these are plates, not rods, thus giving the antenna a bigger surface area for reception. Originally the ARRL bible for antenna design measured gain across full plated (not rodlike) antennas such as this Radio Shack:
As with the Eaglestar and Antop, the receiving elements don’t have to be large. Just sufficient for reception and amplification (their Smartpass preamp is good).
The Antop longitudinal shape (the dipoles are stacked column-wise) gives it a wider beamwidth and sweep than antenna arrays stacked row-wise.
The compact design makes it easily mountable unlike a yagi and placeable within an aesthetically pleasing case. Also the monolithic design of the dipoles (they aren’t an assemblage of separate receiving elements like in a CM 4 bay) gives it added stability.
The great Channel Master 4251 antenna uses the above RS butterfly receivers getting most of its gain from the reflector which pushes the signal onto the four elements.
Of course a lot of this is speculation on my part having looked at the interior design without having the actual engineering specs.
PS The Marathon antenna which people like is of this type.