If it's fun even without full-fidelity, it's fun. But if it's not fun, it might just be the lack of fidelity - not believable enough. I guess one needs an opinion for how much fidelity is enough to know, for the specific mechanics/interactions.
EDIT can always increase fidelity.
Through this discussion, I realize I'm more interested in "feel" than fun as such - e.g. a sense of place, being somewhere, in a walking simulator; or the feel of guns in COD. Not a mechanic; but perhaps a kind of interaction.
Not necessarily "cinematic", but probably more akin to issues in cinema than game mechanics.
I suppose one can still isolate an aspect and iterate on it; but it seems fidelity is important here...