The abstract does clearly mention HVB as being similar to hyperventilation, so presumably it is similar to "bellows breathing" from yoga / pranayama. They also name-check Holotropic breath work, which I have not studied, but has been a hot topic for several years now.
As best as I can interpret, "cyclic breathing without pausing" means no pausing after full inhale or exhale.
By contrast, "box breathing" would have typically equal durations of in-breath and out-breath, with equal duration of pauses. This style of breathing would be done typically to calm the mind, with slow, long breaths.
Breath can also be asymmetrical (typically exhales longer than inhales, said to be calming). I find this style to be awkward, I guess the inhale has to be more forceful to move the same amount of air as will be exhaled.
To be sure, when a topic is posted that people have some interest and experience with, then we will tell you about our experiences. Sorry if that harshes your mellow...