The green curve is a loess curve, which simply smooths the relationship to indicate the basic trend.
The fact that HDI increases with Unbelief percentage does not mean that greater unbelief necessarily causes greater HDI; the causality may run the other way, or both variables may be caused by some other variable, or there may be complicated feedback between the two variables, and probably several other causal factors (which is what I would imagine is the truth).
The identified countries, clockwise from top left, are United Arab Emirates, USA, Ireland, New Zealand, Australia, Norway, Sweden, Estonia, Azerbaijan, Mongolia, Vietnam, Zimbabwe, Dem.Rep.Congo.