The Vanishing of Ethan Carter is something I wanted to play regardless if available on SteamOS or not. I know is now made in UE4 and it should (in theory) come to SteamOS sooner or later, but there was a recent sale on GOG and I couldn't helped myself.
The Steam version should work the same.

The Wine installation is a basic one (wine 1.9.12-staging CSMT) with no extra components installed, just installed the game in a fresh 64 bit wineprefix and use a separate script to launch the 64 bit exec of the game. The game itself is the "old" version made in UE3, the UE4 version doesn't work in Wine...yet.
You can use PlayOnLinux or system's Wine (if you have a newer version on your system).
You can also use a 32 bit install but the textures are limited to Low and there's really no point in playing this beautiful textured game with low textures.

It plays really well with the Steam Controller and the Steam Overlay but (as with other games with proper gamepad support) I prefer to use an Xbox360 controller which also gives force feedback adding to the immersion.

The bad part of this video is that it ends up encoded with the Youtube's terrible standards of quality and makes no justice to the beautiful game graphics. I think Youtube uses a single pass encoder which is really a bad option for high detailed/fast moving videos.

The game is frequently streaming a high amount of textures (no wonder) and is causing stutter especially when played from a rotational disk, your best bet is to use a SSD for this and even then is still happening although with somewhat reduced impact.
For the record the PoolSize trick it doesn't help too much and is the same thing on Windows for this UE3 version of the game. Apparently is something fixed only on the Redux version.

View video on youtube.com