Sure! Here's an example of a single HTML file containing JavaScript that implements the chat game you described:
Chat Game
When you open this HTML file in a smartphone browser, it will display a chat box. Every 2 seconds, a message will appear from "Jimmyflyer242" with a random sentence. Every 3 seconds, a message with the letter "m" will appear from "Thatoneperson40". And every 4 seconds, a message about cats being the best pets in the world will appear from "Jenessapopular7".