What is it about mice and mazes? Generally, mazes have appealed to mankind throughout history. The cultural meaning of them often relates to the paths of life, where humans pass many twists and turns to reach a desired spiritual goal. Animals may not share this view but there are many scientific research methods, where mice and mazes are used to study learning and memory (and where the goal is something more practical, such as a piece of cheese).
Whether this kind of science tells us most about the mice being reserached or the humans doing the research is another matter but the concept of mice and maze is known to everybody and a suitable theme for a game. Thus, it's not surprising that there are many games based on mice and mazes, such as the children's puzzle game Go Getter, the dexterity game Booby-Trap and the video game Mouse Trap.
Given this, it was natural to choose the Mice in a Maze theme for the game. It has a maze, it has a goal, it has traps and it has traps. The players act both as powerless movers (moving as far as they along the only available path) and powerful modifiers (modifying the maze to open new paths) - very similar to the mice and the scientists of the maze research. Who knows, perhaps the scientists' real goal is to get the mice to bring them the cheese?