Saving screens are essential for any games which include a progressive level or storyline. It allows players to return to game states from their previous session.
If a player selects to exit a game, it is good practice to suggest saving any progress that may not already have been saved. Players may be under the assumption that a save state will be automatically made if that is not the case then prompt the user to save.
Online games do not include this feature as they serve no purpose. Often online games will be a new experience every time a game is played.