I'd encourage people to go have a look at the appendices. There are really silly metrics for "happiness". The education ones, for example, are pretty bizarre to just flatly count as "happiness" or believe is a causal agent of happiness. I'm pretty educated and this probably does correlate with my happiness, so it might be some incredibly loose proxy for the concept, but just saying that all else held equal, more educated people are happier seems absurd. Likewise, it includes parental education and other measures that don't seem like they have much to do with anything.
Including inequality as an independent variable is another odd one - if this is actually causing unhappiness, you should already find it in self-reporting metrics and mental health metrics. There's no reason to look at two groups that say they're equally happy and don't show differences in mental health and just declare that the less equal group must be less happy. Well, there is a reason, but it's a transparently political reason.
There are quite a few other independent variables that don't really make sense as independent variables.
The way points are rewarded are sufficiently arbitrary to give the authors the fudge factor to move countries around in the rankings as they see fit.