The website isn't for comedy writers ...
When it comes to plagiarism, the nature/content of a website is completely irrelevant.
If the OP copies the conversation verbatim, technically speaking, he could be sued. Just as I could, if I was to use material from, say, a football forum, without permission.
Unless stated otherwise: the person that submitted the piece originally, immediately gains 'copyright' and ownership of it.
What if you overheard a funny comnversation on the bus and used it in a script? Would that be plagiarism?
No. Plagiarism can only exist (in the eyes of the law) if something has been written down.