Exactly what is considered strictly off-topic there?
Anyone can assume the obvious: NSFW (Not Safe for Work) are off topic, and should be flagged.
Stack Exchange chat rooms are an informal discussion area that have few rules in general, and some 'rooms' have room-specific requirements as well.
In general (from the FAQ):
This site is an extension of The Stack Exchange Network, so discussion should more or less revolve around the same topics you'd find at The Stack Exchange Network — 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.
The 2nd Monitor takes that as a baseline for what's off topic, and extends it (loosely) to exclude:
The Chat FAQ also has the following to say:
Do I have to be nice?
Yes. We expect community members to treat each other with respect … even when they don't deserve it.
This site is collectively moderated by the community through participatory flagging. If your chat messages are repeatedly being flagged by your peers you might find yourself muted, banned, or – in extreme cases – your The Stack Exchange Network reputation may be negatively affected.
If you see an inappropriate, spam, or offensive chat message, please use the hover menu at the far right of each chat message to flag it. This will draw it to the attention of the community moderators.
The 2nd Monitor should always be safe for anyone over the age of 13 (the minimum age of users on Stack Exchange) to see any part of.
If you feel that content is offensive, or spam, then flag that content. The flag will bring the content to the attention of moderators, and other 'trusted' users (random people with > 10K rep). If they agree, the message will be deleted, and the user automatically suspended for 30 minutes.
If conversation is otherwise disruptive, suggest to people to take the conversation to a different room. Alternatively, get the attention of moderators by flagging for moderator attention, or approaching a moderator directly.
As an aside, The 2nd Monitor is known across Stack Exchange as being one of the most welcoming chat rooms. It's in large part because the conversation is closely kept to the above standard Stack Exchange criteria, and keeping things polite, and on-topic.