I was not happy with the way this article started - shame being described as a "damaging, useless emotion that we should neither feel ourselves nor make others feel" - it almost shames one for feeling shame.

It also conflates shame and guilt; while this confusion is common when talking about emotions, the psychiatrist and psychologist authors should know better. To be clear, guilt is about your behaviors, shame is about who you are. They are linked but distinct. Those criticisms out of the way, let's move into the parts of the article that are useful:

So under what conditions does shame end up prodding people into correcting their course? Alternatively, when does intense self-criticism make matters worse by further fueling an addiction (for example, drinking even more to mute the pain of those shameful feelings)?

The article was focused on addiction behaviors such as drug use, but it is useful to think about it in terms of other problematic actions and challenging emotions generally. We have a few reasons for the emotions we experience:

Motivating one's action: emotions make you do stuff.
Communication to others: they convey important information to others without having to actually tell them directly.
Communication to yourself: they tell us important information about ourselves; what is important and meaningful.

With these functions in mind, we can see how we can effectively use our emotions to help us through a situation and make positive changes in our lives. There's a threshold for emotional effectiveness, though, and if you've crossed past the effective threshold you might have a hard time being able to manage your emotion well. In that case, wait for the emotion to become more manageable before trying to use it or deal with it generally.

How, then, can we use the emotions of shame and guilt effectively? Listen to them. If you are feeling lots of these emotions, have a look at what you're doing. If there's something you're doing that doesn't fit into your value system, figure out a way to stop and get help if you can't do it on your own. This is the emotion of guilt.

If you notice you're hiding that behavior from others you care about and care about you, that's also a very big sign you're doing something that doesn't fit into your value system. This hiding is shame behavior. The way to deal with this emotion is to talk about it. Get it into the open. This might result in getting help you need.

Or it might result in getting yelled at and belittled. If that's what is what's going to happen (maybe a conclusion you can draw based on experience), then find people you can share with without fear of further shaming. Support group, therapists, others in recovery. They can all help.

But don't ignore the emotion. This emotional avoidance causes a lot of distress and suffering.