As an AI language model, I can provide you with a basic outline of how you can create a simple game in a single HTML file using JavaScript. However, creating a full-fledged Facebook-like app with an AI game creator function would require a significant amount of code and functionality beyond the scope of a single answer. Here's a simplified example using pictograms to give you a starting point:
In this example, you have a basic HTML structure with a container div for the game. Pictograms are represented as image elements that can be clicked on. The `handlePictogramClick` function is called whenever a pictogram is clicked, allowing you to handle the gameplay logic. The `generateGame` function can be used to randomly generate game levels or other game-related functionality.
Remember that this is just a starting point, and you would need to expand upon this code significantly to create a Facebook-like app with AI game creator functionality.