Freeciv players might enjoy http://longturn.org - Freeciv games where one turn takes a day. Games usually last half a year. We've been playing it this way for ten years now, since around 2004.
I started this comment trying to explain how Civ was not like chess at all, but concluded that the two have much in common.
There's an opening, where there are a few tried-and-true, well studied strategies, and the goal is to claim territory.
Then there's a mid-game, where all available land is claimed, and competing players start trying to steal territory from each other, and capturing the others pieces (or cities).
I can't seem to find a parallel in the end game though, it doesn't require nearly as much planning and cunning in Civ to finish of a wounded opponent as it is in chess.
There is a parallel in the end game: Military advancements. Civilization lets you research new technology for significantly more effective military units, to ease the mop-up phase. The equivalent military advancement in chess is queening a pawn.
The difference is that chess requires continued tactical execution to get there, while Civilization lets you sit back and get there on a superior economy.