Define fun + Fun game

Define fun
One of my favorite games is the Hitman series.

Objectives
The objective of the game is to complete each mission and progress through the story. Each mission there is always a target or targets which the main character, a Hitman, must execute and there may also be objectives you must perform as well. You must figure out how to complete the mission silently making the executions look like accidents and not compromising your identity because you are a hitman.

Obstacles
Obstacles of the game include
Security areas: Sometimes there are security areas which you will need an access card or special disguise to get in.
Security guards: Security guards block you from entering areas, search you for weapons and can attack you.
Innocent people: They can blow your cover, report you, be witnesses. So you have to make sure no one is around when performing a kill or kill the witnesses.

How does the game gradually challenge the player?
The game challenges its player by making missions more difficult, players would have to figure out and learn the area and their target(s) before they make a move, the targets are more exposed making it hard to get a silent kill, hidden targets or disguised enemies and enemies harder to kill. I like how the player has to learn its environment, its surroundings, its enemies and target because it gives the player a chance to come up with their own strategy and plan of attack.
I believe the game is fun because it gives a bit of control to the player, that players can choose a different path to completing a mission. You can either play silent and cause 'accidents' to the targets or assonate them without anyone the wiser or you can go in guns blazing and execute anyone in your way and be reckless.

Defining fun
I believe fun is something that makes you want to come back for more, doing the same thing but having different experience each time regardless of you knowing the outcome. This is what this game does, it has replay value for each mission wanting you to explore more ways to complete it but will always result in the same outcome. Also fun is exploring new ways, this game makes the impossible possible allowing us to explore the way of a hitman and this takes us out of reality and imerses us into a new world and environment.