xinput9_1_0.dll
This file is not a system component: windows itself, not a download. Restore it from the source that installed it rather than downloading a replacement.
The error names your specific file, but the fix is the same for the whole family: the whole DirectX family and the one runtime that installs all of it.
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 oldest XInput controller library, kept in Windows for compatibility with games written before the DirectX SDK versions of XInput existed. It ships with Windows.
Where you see it: Games with Xbox controller support, particularly older or emulated titles.
Windows contains this file, so the error usually means system damage or a game folder containing a fake xinput9_1_0.dll placed there by a controller wrapper such as x360ce. Check the game folder first and remove any copy you find there, then run "sfc /scannow". If the game actually wants the newer libraries instead, xinput1_3.dll comes from the DirectX End-User Runtime, which is a different file with a different fix.
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.