When trying to open Heroes of the Storm, basically since Qhira was released, msvcp120.dll missing bug has been constantly happening. I cannot open the game. Period. I’ve clean uninstalled several times. I’ve ran the scan with the command prompt, I’ve even tried MANUALLY PUTTING THE FILE INTO THE PROGRAM FOLDER and it still doesn’t do SQUAT.
Blizzard Technical Support redirected me HERE to the forums instead of to an actual technical support rep. What I get from that little interaction, is that Blizzard doesn’t even know how to fix their BLATANT MISTAKE and wants the community to. Can any of you give me any advice since they’re unable to? 
check this thread. over there i noted the location where the msvcp files were suppose to be and also support commented in that thread something you might try if moving the files doesnt work for you.
Totally wild suggestion but try running a malware scan. Library files like msvcp120.dll are common targets for malware to infect or tamper with.
Otherwise if Morogoth’s suggestion does not work the only solution might be restoring Windows 10 (effectively reinstalling the OS) and then clean installing HotS.
It is important to note that there are 2 different official msvcp120.dll files from Microsoft. One is for 32bit and the other is for 64bit. They are not compatible with each other. The HotS application might require the 64bit one while the BattleNet app needs then 32 bit one.
These files should be provided by the MSVC runtime installation, if not bundled with the application.