"au fait" is a phrase borrowed from French and usually means up-to-date or up to par.
Here's the definition from The Free Dictionary:
Adj.1.au fait - being up to particular standard or level especially in being up to date in knowledge; "kept abreast of the latest developments"; "constant revision keeps the book au courant"; "always au fait on the latest events"; "up on the news"
Darts is a board game with small projectiles thrown at a bullseye target, and pool is a variation of billiards.
It seems to me that it's being used here to mean "accomplished".
I think there may be a slightly different usage of "au fait" in British English (this can also be seen by comparing BE/AE dictionary entries). I never consider this to mean "up to date"; to me it means "familiar with [e.g. the workings of]", or "having a good or detailed knowledge of" (to quote OED). I thought perhaps it was just me, but this is the only definition the (BE) OED gives.
The primary definition in Webster's Unabridged Dictionary online agrees with you, Matching Mole.
1: fully competent : up to the mark : CAPABLE <he is remarkably au fait in business> <quite au fait at playing tennis> 2: FAMILIAR : fully informed : in touch : au courant <they are always au fait on the latest events> <putting her au fait with what had happened>
Now that I see "au courant" in the second definition here, it does seem strange that we use both phrases to mean nearly the same thing. It seems to me that the "capable" definition is better for "au fait" and the "up-to-date" definition is better for au courant.
I think the author is trying to elide the adverb in the second clause, which you can do to avoid repeating it: "as au fait with darts as he is [au fait with] pool," but I don't think you can elide the preposition, too. I'd prefer: as au fait with darts as he is withpool