Sure, here's a sample chat game using JavaScript encased in script tags in a single HTML file. Please note that in order to achieve the timing for each character's message, I've used random intervals within the given time frame. You can test and play the game by opening the HTML file in a web browser.
In the above game, you will see the chat window (`<div id="chat"></div>`) where the messages will appear. The `displayMessage` function adds the chat messages to the chat window. The `startChatGame` function sets up intervals for each character's message based on the given time frames.
Feel free to modify the game and add your own elements, styling, or interactions to make it more engaging.