Contact the guest again. Say your caretaker saw the extra people, air beds, and tents, and that your caretaker said there are 8 people staying there. (If possible, get your caretaker to take photos, and tell the guest you have photos. You don't have to show him the photos, just say you have them.)
Then say that if you don't hear from him, you will assume there are 8 people and you will be charging an extra __ for the water and plumbing usage, wear and tear on the house and lawn, etc. (Tents chew up the lawn!) Otherwise, he will have to leave as he has violated your agreement, and will not get a refund. Be extra polite, using phrases like "I am happy to have your family as my guests, but this was outside the scope of our original agreement, so I am asking you to be a good guest and reply to my query."
I don't know if you're in a position to kick out the guest (can your caretaker do it?) and it might be easier to just charge the extra. Send a "change of reservation" for the extra amount of money, if Airbnb's system will allow it.
Then contact Airbnb again to keep them up to date on how you are handling it.
Having all your communication go through the Airbnb message system really helps as they can track it there. You can also text the guest at his given number. If he responds by text rather than through Airbnb, reply by text AND immediately respond by Airbnb message also, saying "I just got your text stating that ____." This keeps a record that Airbnb can easily review, and avoids a he said / she said situation.
Be polite, be firm, be persistent. Don't ever lose your temper. Yeah, guests lie, but they're used to doing it at hotels and everywhere else. Saying "I have photos" has always done the trick for me.
And if, for some reason, the guest doesn't respond for days and then is like "Why are you kicking me out / charging me extra?!" you have a good response.: "Because you did not reply to me." Good communication is a cornerstone of the Airbnb host/guest relationship. And at least at that point, they are talking to you! And then maybe you can resolve it somehow.