How is the GOG TLD Linux version upgraded to v338? See no GOG links?

It is necessary to wait until a new installer (maybe there is also going to be a smaller patch) becomes available in the game library here.

Yeah they have to make installers for every platform.
I think (no official word on this yet) that the difference with GOG is that you get the good old installers which take time to make and the GOG team need to test them too (within 24 hours iirc).
So GOG games probably always have a small delay.

Although personally I don't think 2 weeks (previous patch) is really necessary but that is probably related to the much on going bugs fixing Hinterland does. Which is a good thing I think, but it makes the waiting a bit unpleasant haha.