I am just wondering about whether there are any rules about chat topics on Stack Overflow?
When I first entered the PHP chat room, people were talking about music.
Does Stack Exchange monitor this?
All rooms are owned by regular users (anyone can create a room, only a dedicated bunch of geeks can keep one alive and on top of that active).
Some rooms have their own rules (see e.g. Lounge<C++>'s rules and regulations). Some don't. If you don't like a room and its inhabitants, you can always click on "leave".
Chat has a FAQ:
What can we chat about?
This site is an extension of Stack Overflow, so discussion should more or less revolve around the same topics you'd find at Stack Overflow — but in an interactive, less strictly Q&A focused way. Do have fun, but please keep it professional and always be respectful of your fellow community members.
However, traditionally we are much more relaxed with chat's rules than we are with the main site's rules. I don't see why people talking about music in the PHP chat room would be a problem. Nothing stopping you from talking about PHP if you want.
As for monitoring, if you spot something bad happening in chat, use your flags.
What you need to understand is that people are there on their own free will. If they want to help someone, or chat about anything they're free to do as they wish.
They're not obliged to answer your question and the same goes with staying on chat topics.
However, if someone is being toxic to the conversation this is different can definitely get you kicked out of the chat by a mod.