+1 kudo to El Reg writer for keeping as little bias as possible.
Although the finding of "one percent increase in "likes," clicks on links and status updates, the researchers saw a 5 to 8 per cent decrease in their self-reported mental health" doesn't directly give a reasonable/ logical correlation, it is possible that it came from a psychological effect.
Think of Facebook "likes" similar to a tasty snack. For the first few times, you became happy and enjoyed eating the snack. But as you get bored of the same amount of snacks, so you tried to upgrade the amount (by unloading a selfie...maybe). If you succeeded, you get happy again. Except now some users ended up in a trap, where they wanted/ expect the same or more of those snacks. When they are unable to get them, they get unhappy.
Along with the fact that this study has younger adults, it may mean there are people who still care about the numbers of "likes" they receive. We could suggest them to ignore the number of "likes" at one point. Unfortunately, there is no real way to change human behavior (we really like numbers going up), so the best counter is to take a break from it.
Just like the recommendation to get outside, anything not facebook for a while would have helped.