An infinite game is not a game. In order for a game to make sense to the play brain it needs to be simpler than real life and the levers by which the player can take action need to be apparent. It needs to enclose the player and be self-consistent.
The Magic Circle
Johan Huizinga, in the 1938 book 'Homo Ludens', coined the term 'magic circle' to describe humanity's need to separate certain spaces as special and give them rules. The concept applies to everything from sports fields to religious temples. In The 2003 book 'Rules of Play', Eric Zimmerman and Katie Salen adopt Huizinga's term as part of their method creating games, and the term has become popular among game designers as a result.