As an AI text-based model, I can provide you with a basic example of generative art using JavaScript that you can implement in a single HTML file. However, please note that a complete game implementation would require a more detailed specification. Here's a simple example to get you started:
In this example, a canvas element is used to display the generated art. The `generateArt` function clears the canvas and generates random shapes with random colors. The `randomColor` function is used to generate random colors for each shape.
To play the game, simply open the HTML file in a web browser, and you will see the generative art. The art will be regenerated initially and whenever you refresh the page or click a button (which you can add later) to call the `generateArt` function.
Feel free to add more features, interactions, and styling to make it a complete game according to your specific requirements.