Hi, I am Paulo and I'd like to help.
The error simply means that the .exe file cannot be found. Here's how I fixed this problem.
- Navigate to the Riot Games folder and look for a file named "RiotClientServices.exe.old".
- Rename it to remove the “.old” extension, making it "RiotClientServices.exe".
- After that, go to Settings > Apps > Installed Apps (or Programs and Features) and uninstall the Riot Client from there.
See if this works for you.