What defines a maze game?

From Wikipedia
Maze games have a playing field which is entirely a maze. Some may be simple puzzle games in which the player must navigate to the exit, others may be action-based.

An example sub-genre of the action-based maze game is the maze chase game in which the player needs logical thinking to foresee where the enemies come. One must be able to foresee hostile attacks about the flanks to escape from them. The most famous game of this genre is Pac-Man. This genre frequently crosses over with Puzzle, but it often gets by completely without jigsaw puzzle elements and demands only reaction and planning. Notable games include Pac-Man and Ms. Pac-Man
So does this mean a map where there are obstaces to avoid counts as a maze game or does it mean that the players movement has to be restricted based on the walls around them?

PacMan didn't actually use a Maze - so saying the game has to occur within a maze doesn't really count.