@Stephen1478
Oh no. Poor dog.
If the guest is still not responding to messages, it might be time to call him and just tell him politely, but frankly, that this is a real issue and why. Sure, you risk some sort of retaliation, e.g. a bad review, but you will have the right to respond and I think most people would not approve of his treatment of his pet.
I hate when these things happen, but I think a lot of people do not realise how distressed their dog gets when locked up at home all day, let alone in a strange environment. That's not excuse here though as you have been messaging the guest about it.
There is a slim possibility (if you are only sending messages via Airbnb) that he simply hasn't turned on his notifications and doesn't even realise you've tried to contact him. More likely, he's just not a responsible person.