There is currently also no ready-made install-script for the GOG-Version of The Vanishing of Ethan Carter for PlayOnLinux available.

But installation of the game in PoL is very easy, if you pay attention to some details:

1) install a program that's not listed, create a new PlayOnLinux-drive
- choose all three available options (other Wine-Version, configure Wine, install packages)
- I don't use a 64 bit version of Wine, because DotNet is not available for 64 bit.. I'm using Wine version 1.9.23 (32 bit), but others may also work
- configure wine to show a local desktop of 800 x 600 and (important!) capture the mouse in fullscreen
- install packages d3dx9, dotnet40

2) install the game using the GOG-installer
- ignore the error-message at the last install step
- create a shortcut to Launcher.exe

3) start the game for the first time.
- choose your options in the launcher