Requirements
Server Requirements
All API GET and POST requests need to be secure using standard TLS (the predecessor was SSL, now deprecated). Without this most requests will fail. This security is required in order to protect users information and also so that inter-server communication between Anthropics servers and other servers cannot be intercepted.
The certificates used for this need to be the minimum that allow a regular https connection to a web server without warnings about unknown signing authorities (CA), so any of the common CA's can be used such as Verisign. Anthropics often uses the Comodo CA.
It is not necessary for the certificate to authenticate the identity or address of the owner entity, but obviously the certificate does need to be valid for the domain being used and must not have expired.
Put another way, if a browser https GET request to the web server can be made with no errors or warnings, then the certificate being used will meet the Anthropics API requirements.
Client Requirements
The video is accessed via the javascript WebRTC API, which is supported on modern browsers (an exception being Chrome on iOS until Apple supports it).