A theocracy "by definition" involves God (or, more broadly, a religion). Constitutional monarchies do not, necessarily. Furthermore, at one end of the constitutional monarchy spectrum you have the monarch who is purely figurehead with only ceremonial and/or social responsibilities, and the monarchies with high scores in that list are fairly close to that end of the spectrum. (There are also some monarchies right down in the authoritarian end....)

First off, nitpick: I think you meant "lose" rather than "loose".

Secondly, would you mind expanding on your point? I wasn't aware that a country being governed by a monarch implied a theocracy. Sure, you have countries like the UK where the monarch is both the head of state and the head of the established church but that link doesn't have to exist and the existence of that link doesn't necessarily imply any reduction in religious freedoms.

Theocracy?