The gameboard could stimulate ideas for the rules simply by drawing that shape on a piece of paper and looking at it for a while. Before long, a theme develops, add a snappy name and a game is born. Sometimes a word or phrase will trigger game ideas. I've found writing the ideas down as they come to you and then looking at them later can be a very helpful strategy for inventing games. Real events are often turned into games.
Reality can make a great game.
Try making a board game from your own experiences. If you enjoy hiking in the woods it could be fun designing a game about hiking. Maybe there are millions of squirrels in your yard whose acrobatic attempts to get to the bird feeder could translate into a silly boardgame. Perhaps a school science fair, the cafeteria food line or a memorable field trip stimulate game ideas. When designing games, there are no rules and your imagination is the limit.