I was kinda wondering too, and did a (very shallow) dive into the JavaScript on that page. I'm almost positive they are using Deepgram(dot com)'s speech-to-text service.
I ran whisper.cpp on that audio file on my laptop, and it does a reasonably well job too.
Standard audiometry, usually, only produces a test that goes up to 8 kHz (functional speech recognition). An extended high frequency audiometry may, or may not be more revealing as it can go higher. It would have no bearing on your medical treatment though.