I would double check that there is no process called RiotClientServices.exe running. If there is none, then I would try restarting.

If restarting doesn't work, I would recommend reaching out to player support.

As some folks have already noticed, running the installer only installs the login screen unless you actually have access to the closed beta. If you don't have access, it doesn't do anything if you already have League of Legends or Legends of Runeterra installed.