I don't see how this explains depression at all.

that's not the goal of this study?

How is this related to fear, or avoidance, or motivation, or rumination, et.al

Isn't it sort of obvious? Deficits in inhibiting unwanted behaviours, even when aware of the need to inhibit, is a big problem with depression.

Consider rumination or negative self-talk, for example: most people with depression can and do recognize the negative impact these behaviours have on their emotional and mental wellbeing, but they often have trouble "braking" away from these patterns. They know that things might not be as bad as they seem (i.e., a more positive outlook is warranted/realistic), but they can't inhibit these thoughts.

Motivation is the same thing: think of an individual with depression who can't find the motivation to get out of bed, to leave the house, to look for jobs, etc.. In most cases, this person will recognize the need to do these tasks (i.e., the need to change their behaviour - to inhibit their current behaviour patterns), but they might not be able to muster enough motivation to accomplish these tasks.

Avoidance: "I know I need to apply for jobs and find work, but I don't have it in me to put that work in..." "I know that staying in bed all day isn't helping, but I can't get out of bed..."

The thing is that depression, or the maladaptive behaviour patterns linked to depressive states, can act like a rut. Someone with depression can and often will notice this rut (i.e., they can recognize the damaging effects of their habits, behaviours, attitudes, etc.), but breaking free from this rut (i.e., creating positive change for these habits, behaviours, attitudes, etc.) might not exactly be possible without help.

The study found in OP's link seems to offer a pretty simple, experimental take on this kind of stuff. It doesn't really take much to see the conceptual links between the researchers' experiment, and behaviours exhibited by individuals with depression.