Unwinnable Joke Game

An Unwinnable Joke Game is a game that has a clear win condition, but this condition cannot be reached, and this is intentional on the part of the designer. These are almost always meant as a joke.

Compare Unwinnable By Mistake, where the game cannot be won because of a design flaw, Unwinnable by Design which is a serious game that is designed so that certain circumstances will render it unwinnable, as well as Endless Game and Wide Open Sandbox, which don't have a win condition in the first place.

Certain gambling machines may fall under this trope, but most countries have laws against slot machines that never actually allow you to win the jackpot.

Examples of Unwinnable Joke Game include:

The infamous Scary Maze Game is an online prank where your goal is to manuever your way through a maze, but the third level is impossible to beat as, when you get to a certain point in the third level, a close-up image of Regan from The Exorcist pops up and screams.
In Steamshovel Harry, the Earth will be destroyed by a missile in ten minutes, and only you can stop it! The tutorial takes 9:58 minutes, and you lose immediately afterwards.
Super Kingio Bros is a version of Super Mario Bros with the King of Town replacing Mario. Unfortunately, he can't jump high enough to pass the first Goomba, so it's probably just as well that you don't actually get the three lives shown.
Xkcd has a strip about Tetris. Predictably, someone on the internet made a game like that. And some managed to score lines in it.
Zephyr Skies: The Winter Sage starts out as a typical rpg, but then it glitches and turns into playing tetris/matching up pictures. It may actually be winnable in terms of getting perfect score, but the results don't change and the game repeats in an infinite loop.
Most Remar Games have a highest difficulty level called "Reallyjoel's Dad" that is completely impossible. Examples include Hero Core, Iji, and Hyper Princess Pitch.
The creators of The Room: The Game released what appeared to be the equivalent for The Hunger Games... on April 1. It becomes a test to see how many times a player can take one of Clove's throwing knives to the head before giving up.
An in-universe example appears in the Britcom Mr Don And Mr George. The two titular characters are shown playing a board game, which George is winning by declaring a series of increasingly bizarre moves. It is then revealed that Don never gets any moves, and the game is called "George, You're Simply the Best."
Every single Luna Game.
The Interactive Fiction Suspended becomes this if you play on Impossible mode, where the sun goes nova in two turns.
Likewise, Penn & Teller's Smoke and Mirrors has its own Impossible Mode, where Lou Reed appears and kills the duo, then tells the player, "Impossible doesn't mean very difficult. Very difficult is winning the Nobel Prize; impossible is eating the Sun."