Most of those dimensions can actually be classified as "towards" or "away", though, which will be part of the subject of the next post in the series.

The important distinction for humans, though, is that emotions are "somatic markers" -- meaning that they are distinctions in the body, for purposes of organizing action responses. They aren't arbitrary scores, but more like "action stances" of varying degrees. So yes, they're multi-dimensional and all of the categories you mention (e.g. "intellectually interesting" and "enough sex") qualify... but they also largely group into (and layer on top of the machinery for) the somewhat-more-fundamental operators of "toward" and "away".