This may be excessive nit-picking, I'm not sure; but I just don't think that your examples of the Connotation Game provide connotations as you define them. "demagogue" and "eloquent" have different denotations - it's not just the emotional aura of the words, their actual meanings are different. Ditto for "patriotic" and "jingoistic" and so forth. The point of the game is that the same person/act can be described by flattering, neutral and disparaging words, but even though the same behavior is described by different words, the meanings of the words are different. The game points out inherent subjectivity present in those meanings.

If you used e.g. "black", "colored" and "African-American", then it'd be about connotations. But that's not how the game is played.

More generally, I think you're trying to give the concept of a connotation a larger role than it's used to. Connotations are about differences in phrases like "ultra-rich", "stinking rich", and "independently wealthy". In the phrase about the ultra-rich you quote, it seems difficult to assign the subtext being carried to connotations, unless you want to use "connotation" in the sense of "subtext, any implied meaning". But I don't think those shoes will fit the word.

Subtexts are very important, and are used insidiously all the time. They're not always emotional; sometimes they exploit logical structure, as in the canonical example "Have you stopped beating your wife?" It's difficult to stand your ground against them, and forcing them into the open, demanding that they be made explicit, as you suggest, is a useful technique. Unfortunately, it usually won't work on someone who feels entitles to use a subtext against you - due to either intentional demagoguery or misguided self-righteousness, for instance.

One framework that seems to make a careful study of implied meanings is that of framing. I don't really know what they're doing with this and whether it's more than a useful metaphor. But, to repeat myself, I think that "connotations" might be too straight a jacket to use for the notion.