This is the "Rock Bottom" of fixes—it almost never fails. Steam has a built-in tool to compare your game files against the master version on their servers.
Steps:
Time required: 3 to 10 minutes.
If you search for "Steam Api 64 Dll download," you will find hundreds of sketchy websites offering a standalone download. Do not use these. Steam Api 64 Dll Wwe 2k15
Downloading DLLs from third-party repositories is dangerous for three reasons: This is the "Rock Bottom" of fixes—it almost never fails
Always let the official software (Steam) manage these files. Time required: 3 to 10 minutes
If the above steps don't work, you might consider reinstalling Steam. Be sure to backup your steamapps folder (which contains all your games) before doing so.