I'd recommend studying physics, because of the problem solving skills it teaches, and how it helps understand the complexities of the world. (But then i would say that as a physicist)
As for intelligence, it really means 'those mental abilities which our society deems valuable'. Hence the theory of multiple intelligences postuaktes ~8 :
musical-rhythmic intelligence (which i have almost none), visual-spatial (where i'm above average), verbal-linguistic (where i am about average), logical-mathematical (where i am considerably above average), bodily-kinesthetic (where i am at most average, but it is typical to assume most professional sports stars are above average), interpersonal (ie understanding other people, a part of emotional intelligence, where i am probably below average), intrapersonal (understanding yourself, the other part of emotional intelligence, where i am again below average), and naturalistic (which is about understanding nature and natural cycles, which farmers supposedly possess).
Of course not all members of the forum, or any group will accept that all the types of intelligence are actually valuable to society. And thus reject them as types of intelligence at all. But such an arguement is largely semantic.
Intelligence as an idea is constructed for social purposes. Why do we value it? What social purpose does it serve? As is the opener's question.
The fact that diplomacy palyers are above average intelligence is not surprising. We are a group of people who are interested in a very challenging board game (i think harder than Go, or Chess) which tests multiple types of intelligences, from the inter-personal, to the logical, to the verbal-linguistic (except in gunboat perhaps).
So we are intelligent because we are a self-selecting group of people who share intelligence as a common trait.