These are just skills. No one has proven they take some special kind of intelligence or that such intelligences exist, including oft-quoted emotional intelligence.
This isn't true. We have overwhelming evidence that these "skills" originate in different parts of the brain in all humans and if we disable those parts, those "skills" disappear. Those parts of the brain are unique and have their own structures. There is strong evidence that they require unique "hardware" and as such, are a "special kind of intelligence".