I think you're right to want people to be off the cuff, and also relaxed. I would personally try to emulate the traditional phone interview, optionally with video -- start off with some chitchat and background on the company to get candidates comfortable, and then ask questions which demand immediate and realtime, unrehearsed responses.

You have the chance of making the process more efficient, especially when there are hundreds or thousands of applicants. Maybe use a video pitch by the interviewer, clip about the company, etc. to set the setting and make the candidate comfortable, and then do instant-response questions with video response.

I might also start the interview with some super-softball questions, to get the user familiar with the system. "What's your name?" isn't really good, but some really easy tech questions or even general knowledge questions might be good.

The main benefits to me in having a bunch of recorded interviews is that I can instantly drop one if the candidate is obviously a reject. It took me a few years of hiring responsibility before I got to the point of "I'm sorry, I have to end this now" if someone is obviously unacceptable 5-10 minutes in. A problem with doing that in real life is that you need to block out the whole interview on your schedule, and it's harder to fit other things back in once that is freed.

Being able to outsource reviewing answers to other people in your organization would also be great -- e.g. sending the database question to your database guys. If you are really interviewing 1k people, you can have your database guy look at 10, grade those, and then have a junior person, based on those, grade any which pattern-match well, and refer the others back to the expert.

I'd still prefer a written or executable test for most technical jobs, at least as my initial screen, and an IM or phone chat, but I could see the value of this for some roles.