Rowanism: As for the Linux installers: I asked Matthias and he said Linux on GOG is currently not available. What installers did you find, SteamOS ones?
Nope. When I open the Game's page in my GOG library and set System to Linux, I see something like this (also see screenshot):
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Game installers and updates:
Chained Echoes 1.342
DLC Installers
Ashes of Elrant 1.342
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I downloaded both and ran them. The first installs the game, and from the contents of the folder Chained Echoes/game/Chained_Echoes_Data/StreamingAssets/aa/StandaloneLinux64 it definitely contains assets related to the DLC.
The second seems to install a readme.txt and at least another file that should unlock the DLC, but does not.
So if the Linux version is not yet meant to be available on GOG, maybe those are test builds that should not be publicly visible? Aside from the DLC not showing, game seems to run fine, though, loading my old v1.1 saves without a hitch.