Hello guys,
Here comes small update solving local saving issue. If you are one of those unlucky players who have problems with steam cloud progress saving, we are offering you a hack.
Launch the game with "--nosteamcloud" parameter (right click on the game in steam library > Properties > Set launch options... (in General tab).
Now in main menu screen in bottom right corner should be written "steam cloud disabled" and progress should saved locally.
Thanks to @axios2006, @Willit and many other players for pushing this feature.