I too had the same issue after installing battlefield 4 through the EA app, I repeat through the EA app not steam, if you installed through steam, then that may be the issue. Anyways here is a rundown of what I did, from purchasing all the way to managing to run the game finally:
1) Bought battlefield 4 premium edition through EA site, not steam
2) After buying it, I was prompted to install EA app for desktop
3) Installed EA app
4) Downloaded and installed the game on the EA app
5) After installation was complete, I clicked Play, didnt work, I was given the SMVC120.dll error message
5) I decided to repair the game found in the "manage' tab found right next to where you can click play on the EA app
6) Error message dissapeared, now the game just loaded for a second with that orange loading thing on the EA app and nothing would happen
7) Was told to install microsoft visual c++ 2013 x64, wasn't specified the version, this will make sense later. After installing the random 2013 version of Microsoft visual c++2013 x64, the game would do the same.
8) Ended up installing a second visual c++ 2013 directly from battlefield 4s game files, found on the first file, just look for anything that says visual c++2013 x64
9) Decided to clean boot my pc link: https://support.microsoft.com/en-us/topic/how-to-perform-a-clean-boot-in-windows-da2f9573-6eec-00ad-2f8a-a97a1807f3dd
9) After that I have no idea why, but decided to install again visual c++ 2013 x64 only this time version 12.0 link: https://learn.microsoft.com/en-US/cpp/windows/latest-supported-vc-redist?view=msvc-170#visual-studio-2013-vc-120
10) After installing this it worked, I am not sure if it is the clean boot that fixed it, or the installation of microsoft visual c++ 2013 x64 12.0, but it worked