mplf100: XCOM 2 wouldn't start (playing the "PLAY" button would grey out and simply come back to green).
System: Windows 10, 64x
How I fixed it (or worked around the issue):
in C:\Windows\System32
copied msvcp120_clr0400.dll to msvcp120.ldd
copied msvcr120_clr0400.dll to mscvr120.dll
copied vcomp140.dll to vcomp120.dll

Now the game runs to at least the Startup screen. I do not know if this will cause grief later on in the game.
Disclaimer: I do not understand the impact this may have on other executables on the sytem. I wish the workaround was localized to the XCOM 2 executable.

How I got there:
1. My first installation was interrupted by a system shutdown. Not clear if that didn't put the system in a bad state for this game.
2. Two re-installations and a "verify installation" didn't solve the problem.
3. Attempted to "Launch XCOM 2" from its installation directory, that is when I could see it complaining about the missing DLLs.
4. Noticed the similar DLL in the system32 directory and did the above copies. Works so far...
YMMV

mplf100: XCOM 2 wouldn't start (playing the "PLAY" button would grey out and simply come back to green).
System: Windows 10, 64x
How I fixed it (or worked around the issue):
in C:\Windows\System32
copied msvcp120_clr0400.dll to msvcp120.ldd
copied msvcr120_clr0400.dll to mscvr120.dll
copied vcomp140.dll to vcomp120.dll

Now the game runs to at least the Startup screen. I do not know if this will cause grief later on in the game.
Disclaimer: I do not understand the impact this may have on other executables on the sytem. I wish the workaround was localized to the XCOM 2 executable.

How I got there:
1. My first installation was interrupted by a system shutdown. Not clear if that didn't put the system in a bad state for this game.
2. Two re-installations and a "verify installation" didn't solve the problem.
3. Attempted to "Launch XCOM 2" from its installation directory, that is when I could see it complaining about the missing DLLs.
4. Noticed the similar DLL in the system32 directory and did the above copies. Works so far...
YMMV

way2hungry: Tried the steps (there's a few typos in there btw) but they didn't work for me neither. Tried a fresh install too, but no joy.

Have installed the various VC++ redists (both x86 and x64), and restarted, but no joy.
No logs present, and doesn't work trying to run the pure game exectuable as an admin neither

Win10 Pro x64
RX 580
Ryzen 3100

doresainlichking: I managed to handle the problem, my game is running.

In case your problem is similar:

I cleaned my computer and started fresh,
updated to latest framework .net
installed microsoft visual C++ 2012 and 2013 (both 32 and 64 bits)

and it's now working. Hope you find a way to solve your issue