In the log there is an error message "Loading assembly failed: "Managed/Assembly-CSharp.dll""
Searching the net for that error I only got one hit with an actual "solution": https://steamcommunity.com/app/383120/discussions/2/355043117505214343/
In that thread (about a different Unity-based game) people got rid of the bug by reinstalling windows. The theory was that some wrong unity settings were stored somewhere deep in windows (probably in the registry) and could only be removed by a complete wipe of the PC.
This may not be the case here, but it might be your last option if everything else fails.
Things you can do first:
0) Make a backup of all your important data !!!!!!!!!!!!!!!!
1) First make sure you have only one copy of the game installed and in use. We don't want to inspect one copy and start another for example.
2) Check whether the file Assembly-CSharp.dll exists in ...\7 Days To Die\7DaysToDie_Data\Managed and is readable and has a size somewhere around 6Mbyte(?). Also validate the client through steam, even If you have done it before.
3) If you have some other unity games, update them and run them. Do they have problems too?
4) If you have very old unity-based games or programs (without any newer versions available) on the PC, try to delete them and their data as best as you can.
5) Search your harddisk for directories called "unity3d", "unity", Unity3D"... If you find them and they are not subdirectories of other games, change their names to "unity3d.off", "unity.off", "Unity3D.off". Start the game and see if it helps. If not, rename them back to "unity3d" ...
6) Wait for better ideas to surface. Someone else might have a better idea than what I posted here.
7) This is a very risky step with low chances of success: Use regedit to search your windows registry for settings with unity in the name. If you are brave, try to delete some of them and see if it helps. You could damage windows by doing this, so be prepared to reinstall if this doesn't work out.