It is indeed a bot, as I've discovered. I had a theory that we were randomly interacting with people that were visiting the site, but I know now that it's answers are based off of a pattern.
Here's my experiment in how I found out:
Type in the phrase "Screw the rules, I have money."(Yugioh Abridged quote)
It will answer with "But that's against the rules."
Repeat.
It will answer with "You didn't follow the rules."
Repeat
It will answer with "Yugioh."
Repeat
It's answer cycle repeats over and over. This one has three, but it wouldn't be surprising if more common phrases had more programmed into the site. Either way, its pre-programmed. Its very thorough, but it's a bot nonetheless.
EDIT: Its even more advanced than I thought. Cleverbot can learn from people's responses and use them itself.