I am not sure what to call that type of ejection since the term "hand ejector" is usually associated with S&W, who used it to describe their swing out cylinder revolvers. Iver Johnson called it just manual ejection, which is about as good a term as any.
There were two reasons for it. The first is that it is simply cheaper, eliminating several parts and the associated fitting. The second is that the conventional cam type ejector used on top break revolvers has its limits due to limits on the length of the cam. If the cartridge is short, it works OK, but at some case length the cam won't fully extract, one of the reasons top break revolvers are not made for long cartridges (strength, or lack of it, of the top break frame is the other).
There are ways around that in a topbreak. The old S&W Russian and Baby Russian used a cogwheel system that was more complex than necessary but they soon went to a cam system.
Jim