Path.Combine(Application.StartupPath, "файл_игры.exe")

private void play_Click(object sender, EventArgs e)
         {

             string path_name = @"C:\Users\Администратор\Desktop\The Real Life";
              
        Process game = new Process();
          game.StartInfo.FileName = "The Real Life ALPHA 0.5.exe";
             game.StartInfo.WorkingDirectory = Path.Combine(Path.GetDirectoryName(Assembly.GetExecutingAssembly().Location), path_name);
            game.Start();

         }

private void play_Click(object sender, EventArgs e)
          {

               string path_name = Application.StartupPath;
                
               Process game = new Process();
               game.StartInfo.FileName = "The Real Life ALPHA 0.5.exe";
               game.StartInfo.WorkingDirectory = Path.Combine(Path.GetDirectoryName(Assembly.GetExecutingAssembly().Location), path_name);
               game.Start();

          }