I finally figured out what the problem is: I didn't follow the tutorial close enough, and I thought it had to do with differences between RGSS and RGSS2.

Fixed script
CODE
class Advanced_Window < Window_Base
  #-----------------------------------------------------------------------------
  # * Object Initialization
  #-----------------------------------------------------------------------------
  def initialize
    super(0, 0, 100, 100) # x, y, width, and height of window
      self.contents = Bitmap.new(width - 32, height - 32) # Content field (Bitmap)
      refresh # A method defined below
  end
  #-----------------------------------------------------------------------------
  # * Refresh
  #-----------------------------------------------------------------------------
  def refresh
    self.contents.clear # Clears Bitmap in preparation for content
    window_content # Draws content within the window
  end
  #-----------------------------------------------------------------------------
  # * Window Content
  #-----------------------------------------------------------------------------
   def window_content
     actor = $game_party.members[000] # Increment from right to left: (001)
       self.draw_actor_name(actor, 0, 0) # (variable, x, y)
       self.draw_actor_hp(actor, 0, 25)
       self.draw_actor_mp(actor, 0, 50) # Changed from SP
#~     self.draw_actor_exp(actor, 0, 75) # This doesn't work in VX without more work
   end
end
#===============================================================================
# * End File
#===============================================================================