Will a user get punishment on breaking thread rules set up by the OP?
For example, if I make a thread about some serious topic in off-topic board and I set a rule saying not to make funny and non-contributing posts, will a user get punished for breaking that rule?

Well i think its like when at market thread when you put tc only
and someone offers an item you get a warning
so probably i think that person will get a warning or something

I wasn't specifically talking about market board.

I know but it was just an example i think you get a warning if you break a rule of that thread

I wonder about this as well, I think you can say it like i.e.

"If you don't follow these rules I have the right to tell you to gtfo".

And if they didn't you could report'em.

It is implied that anyone replying should match the Ops seriousness and it's a given that posts should be contributing and discussing etc...

Since Offtopics is a mild discussion board anyway, noncontributing posts are already punished.