Using Arch Linux (64-bit), with version 2.0.4 and all DLC installed, my main campaign progress is not saved properly. I haven't tested the other campaigns yet.
Saving/loading games works without any problems, the home realm is also saved correctly. Every time I restart the game, all maps are locked again and no achievements are available. Basically this means I'm replaying the tutorial every time.
Using the tutorial level, I've tested that I can load a game, complete that level and then the progress will be recorded until I quit the game again (i.e. I can start level 2 correctly).
Some bits that are saved properly are: all the (graphics/audio/etc) settings, whether the intro movie has played the first time, and the help button tutorial in the first level doesn't come back after the first time either.
I have the game installed to a custom directory (on a separate partition; full install path is /mnt/linux-games/war_for_the_overworld -- no spaces). I did make sure my Linux user account has write access to the entire directory and all files (in fact, I installed the game as the same user).
I also tried removing the entire directory and then reinstalling the game from scratch, but that has not solved the problem.
Player.log file of completing the first level (which should save progress): Player.log.save
Player.log file when restarting the game: Player.log.load
Based on file timestamps I can see that my custom save, and the WFTO_Tutorial file were saved when finishing the level. Options.txt is also properly saved. You can download the full GameData directory as a zip from here (link will expire November 7th 2018).
Customer support service by UserEcho