I wonder whether or not there might be a prime example of the game of general expertise par excellence out there, one that touches on many domains simultaneously...
Probably not. While in video game design there are general competencies you can rely on, there are both mutually exclusive challenges: fast paced FPS games like Quake 3 cannot be played like slower paced FPS games like Call of Duty, players who attempt to transfer their skills without understanding this don't succeed; and balance problems, where the addition of game elements overshadow others like in Alien Swarm where there are five effective weapons even though there are fifteen other options and some of them are dismissed unfairly because they are introduced to players who haven't seen a need for the skills they ask. Both of these factors, however, mean that challenges and tradeoffs go hand in hand in your game's design.
That all said, people do try. Spore is the readiest example of this to me: the mishmash of different games doesn't really work, the way they tried to address the challenge balancing issues means that four fifths of the game design is effectively useless, but it's an instructive game nonetheless.
Excuse me for waxing over-philosophical in my last message, since I said "might be" rather than "currently is". To be clear, I'm referring to the practical possibility (if not the straightforward logical possibility) of such a game existing.
I suppose, in any case, that one form such a game has the greatest chance of succeeding in meeting that (rather vague) designation would involve its exhibiting the most generality within its gameplay, such that the kinds of cognitive requirements put upon users would not necessarily involve specific ...
http://blogs.scientificamerican.com/observations/2011/12/01/how-a-computer-game-is-reinventing-the-science-of-expertise-video/