steam_api64.dll
This file is not a system component: supplied with the game by steam. Restore it from the source that installed it rather than downloading a replacement.
If the file is already there and Windows still complains, read the message again: “entry point not found” is a different problem from a missing file, and installing the runtime again will not solve it.
And if the box says RUNDLL rather than naming a program, the fix runs the other way: something left an instruction behind pointing at a file that is meant to be gone, so restoring the file is the wrong move.
Do not download this DLL on its own
Searching for a missing DLL by name leads to sites that hand you that single file. It is one of the oldest and most effective malware delivery methods there is, and a system DLL from an unknown source is indistinguishable from a deliberately modified one. There is never a legitimate reason to obtain a runtime component that way.
The same goes for the tools that offer to do it for you: what a DLL repair tool can and cannot actually fix.
What it is
The 64-bit Steam API library. Like its 32-bit counterpart it is not a system component: it lives inside each game folder and Steam installs it with the game.
Where you see it: A game failing to launch after an interrupted update, or after antivirus quarantined a file it did not recognise.
In Steam, right-click the game, choose Properties, Installed Files, then Verify integrity of game files. Check your antivirus quarantine too. This error is also extremely common with unauthorised copies, which is why so many sites offer the file directly, and downloading a replacement steam_api64.dll is one of the most reliable ways to infect a machine.
Why there is nothing to download here
There is no verified download we can offer for this one, because installing a file is not the fix. The steps above are what actually resolves it. That distinction matters: the sites ranking for this file name are selling a download that would not have helped even if it were safe.