I had read the FAQ and navigated to that location, but there is no replay folder - the closest is "AutoRecord-SinglePlayer", but placing the file in there does not make it appear in the watch games list.
I assume that a new folder would need to be created named Replays or the suchlike, but I do not know what it ought to be called.
As a test I recorded one of my own games and saved it, but could not then find the record file in C:\Documents and Settings\username\Application Data\Ironclad Games\Sins of a Solar Empire\ but that one does show up in the list of recorded games, so I have no idea where the game has put it.