Categories of Board Gaming skill
A list of categories of board game skills isn't something I've ever seen.  To actually come up with one, I think you have to first start by looking at research from the psychology field in relation to the different forms of IQ.  The theory of multiple intelligences that was created in 1983 by Howard Gardner breaks out different types of intelligence.  Gardner lists 8 different types of intelligence.

Depending on the type of game, I would say some of those intelligences come into play.  Certainly if you have bodily-kinesthetic intelligence and interpersonal intelligence, you would be more likely to be a shrewd trader in games like Settlers of Catan.  If you can read people's body language to tell they're bluffing, this is a huge leg in games like Poker.  On the other end of the spectrum, spatial intelligence would be incredibly important for games where board position is important.

There is also how much planning people do to consider.  Good chess players, look ahead at more possible moves then weaker chess players, and a similar ability to analyze future events would be a good thing to look at.  This gets into game theory and prefect play.  A players ability to practice this would be another big skill.

Speed would be another topic to consider.  Players who arrive at decisions faster would also be better at games where timing matters.  This could also affect games where timing may not immediately be apparent.  Being able to realize any deal another player is offering before the others players accept, would usually be beneficial.

Since research on psychology and artificial intelligence should also be considered, I personally don't feel qualified to give you an exhaustive list.  There is a book, Moves in Mind: The Psychology of Board Games you might be interested in if you really want to delve deeply into this topic.  There is current active research by psychologist and programmers for using games to develop different skills in participants that looks at this question from a different angle.


Promoting Broad and Stable Improvements in Low-Income Children’s Numerical Knowledge Through Playing Number Board Games
SIDES: a cooperative tabletop computer game for social skills development