I want to be able to play the game N, but I can't figure out what to use other than archive manager to open it.
A .tar file is an archive, similar to a .zip file. It is compressed. As with a .zip file, you have to extract (decompress) the contents.
You can extract the contents with any of several graphical tools, archive manager is fine, or from the command line as follows;
Usually there will be a README explaining how to use the contents of the archive to play your game. Once you have finished extracting your archive, the contents may or may not need to be compiled. Here is a quick guide on compiling an application on Linux.