What game is this?
You open rar files the same way you open zip files -- only you need a program that recognizes rar files, like 7-zip, WinRAR, or Winzip. Windows itself can only open zip files, and not other types of archive files. 7-zip is free. You can download 7-zip from http://www.7-zip.org/
Did the game actually install, or did it only extract? Did you see the installer running automatically after unzipping it?
Some games don't actually have installs. You just extract them (whether from zip or rar) to where you want them and then run them by double-clicking the game exe. If they don't show up on the Start screen, you can add them manually after locating the game exe.http://www.bleepingcomputer.com/tutorials/add-remove-programs-windows-8-start-screen/