I'd probably check that Origin Games\Battlefield 1\__Installer\vc\vc2012Update3\redist\vcredist_x64.exe   and   Origin Games\Battlefield 1\__Installer\vc\vc2013\redist\vcredist_x64.exe have both installed properly and do a repair install on them. Sometimes they get bored and want you to repair them.

Have you checked if you have .Net 3.5 (dotnetfx35.exe) and .Net 4.5.2 (NDP452-KB2901907-x86-x64-AllOS-ENU.exe) installed in Windows? I think you need them as well as any Visual C++ redists' that come with games in order for them to work. Some releases of Windows don't install .Net 3.5 (dotnetfx35.exe) and you have to do it yourself even though it's on the disc or ISO, and much of the Windows Store stuff needs it to work and whole bunch of other apps. It used be a real pain to do but I hope they fixed it and it will just install now as that was many months ago, but there are guides how to install it if you do a search on google or something. But hopefully .Net 3.5 should install fine and then the BF1 update should work.

If you look in Windows Control Panel> Programs and Features, the Microsoft Visual C++ redistributables which are already installed should be listed there, including Microsoft .Net Framework 4.6.1 if that is installed, but Microsoft .Net Framework 3.5.1 is likely hidden in "Turn Windows features on or off" and if not you probably have to install it.

Microsoft .NET Framework 3.5

https://www.microsoft.com/en-us/download/details.aspx?id=21

That's a real legit link too by the way.