Sure, here's a simple HTML game implementation that meets your requirements:
Welcome to the Name Judgment Game!
To play the game, simply open the HTML file on a smartphone or any web browser. It will prompt the player to enter a name, and based on the name's first letter, it will display a judgment message accordingly. If the name starts with 'C', it will display "That's a bithes name." If it starts with 'J', it will display "Noice!". If it starts with 'A', it will display "Mega dope!". For all other names, it will display a randomly selected response using the `getRandomResponse()` function.
Note: This is a basic implementation of the game and can be expanded upon with additional features if desired.