Saudi Arabia is blank in that table for "World Bank GINI", which is otherwise the most populated. There is the "GPI Gini" but only a few countries have that, and there seems to be little correspondence to show where Saudi Arabia may be inserted.
Sorting by "World Bank GINI", you are right that at the low end there are a number of former Soviet republics mixed in with the expected EU countries (Denmark, Sweeden, Norway, and Austria are lowest). I think the history of these countries may make them somewhat unusual. Much more relevant to your point is some unexpected ones, such as Egypt and Iraq, nearer the low end.
The other end of the table is more interesting. It is pretty clear that lower income inequality is a requirement, though, as you state, not the only requirement, for democracy.