Putting aside the fact that it is just an insecure and undignified way of transferring data. Why not host the 'video proof' site on namecheap domain? so you know who's watching. And why not ask for photo ID instead of credit card? I mean anyone can send an email "go to [whatever] domain and show me your credit card, or I'll stop your [whatever] service" and NameCheap users will be conditioned into falling for this scam. Its reckless and unprofessional.
And i don't know how else to define took some of my money and registered a domain.. then kept it cause that's what happened. You have a deadline to do your cam show, which is shorter than the time their support service takes to answer an email about your concerns; After that you lose some of your money and your domain.