So there is a mechanism that looks at the problem and then picks the subsystem to delegate it to. Is it a game of chess - boot up the chess program? Is it poetry? Boot up the poetry generator.

No, that's not actually a good description of the mixture-of-experts methodology. It was poorly named. There is no conscious division of the weights into "This subset is good for poetry, this one is best for programming, this one for math, this one for games, this one for language translation, etc."