To reproduce:

1. Open the project, attached by user (bugFogMode.zip)
2. Open "main" scene
3. In Play mode, press any key
4. Observe how fogMode changes
5. Build the project for standalone
6. Launch the build
7. Press any key
8. Observe how fogMode changes

Expected: changing fogMode at runtime works both in the Editor and in the build
Actual: setting fogMode to anything else other than Linear at runtime does not work in build

Reproduced in 5.4.5p2, 5.5.3p2, 5.6.0f3, 5.6.1p1, 2017.1.0b6, 2017.2.0a1

By design: other fog variants aren't detected in the project so they aren't built to save space. It is possible to force the fog variants you want to package in your build. Go to "Edit -> Project Settings -> Graphics", scroll down at the bottom and you should see a "Fog" dropdown set to "Automatic". Switch it to "Manual" and check the variants you need.