> How do you measure the capacity for improvisational comedy?
What makes something funny? Usually, it's by subverting someone's predictions. You have to be good at predicting other's predictions to do this well.
> How do you measure a talent for telling convincing lies?
You have to explain a phenomenon better than the truth to convince someone of your lie.
> How do you measure someone's capacity for innovating in a narrative medium?
As in, world-building? That is more of a memory problem than an intelligence problem, though you do need to be good at compressing the whole world into what is relevant to the story. People who are worse at that will have to take more notes and refer back to them more often.
> How do you measure someone's ability for psychological insight and a theory of self?
They are better at explaining a phenomenon (their self).
> How do you measure someone's capacity for understanding complex, multi-faceted irony or picking up subtle social cues?
Refer to the above. Also, using the adjectives 'complex, multi-faceted' is lazy here. Be more introspective and write what you really want to say.
> Or for formulating effective metaphors and analogies, or boiling down concepts eloquently?
Compression = finding short programs that recover the data.
> How about for mediating complex, multifaceted interpersonal conflicts effectively?
Quite often not an intelligence problem.
> How do you measure someone's capacity for empathy, which necessarily involves incredibly complex simulations and mental models of other people's minds?
"incredibly complex simulations and mental models of other people's minds," however will you do this? Oh, I know! Your brain will have to come up with a small circuit that compresses other people's brain pretty well, as it doesn't have enough capacity to just run the other brain.
> Do you think excelling in any of these doesn't require intelligence? You sound like you consider yourself quite intelligent, so are you excellent at all of them? No? How come?
I am actually pretty good at pretty much all of these compared to the average person.