OpenGeofiction is a user-made world map of a fictional world, created using the OSM software platform.
This project has its own enforced policy: its purpose is a pure artistic creation project (or game with its rules) which forbids using any data representing real object on Earth. Even the displayed names must be invented.
The map is in constant evolution (work in progress), it may evolve over time more rapidly and more dramatically than what occurs on real Earth. It has its own imaginary local events similar to what exists on Earth: hurricanes, floodings, volcanoes, political events, dictatures or democratic processes; islands or continents may appear suddenly or disappear completely; cities may be destroyed or replanned completely differently by their authors in their approved area of work; shipping lines or roads may appear or disappear, a previously dry desert could become a rain forest...
As this uses the same toolset, tags, etc as OSM, the real osm world map could be used the same way.
Actually there are existing games which use osm as a map. In 112 Operator you play as an operator and you have to send rescue forces to real locations on osm. At the beginning of the game you can select any real city in the world: https://store.steampowered.com/app/793460/112_Operator/