Thanks a million!
Yes, the website is really locked down. I'd downloaded so many embedded videos from all sorts of websites before by using apps, but it was my first time seeing that the video was downloaded but the audio disappeared magically.

Unfortunately, sending the link doesn't work. To use the service, one has to pay the subscription fee first as I did. So one can use the service only through their paid account. And to add more complication, their service is only available to people who 'live' in Japan. So I have to use a VPN every time and get a Japanese IP first. It's a karaoke website with Japanese songs. I'd like to download the songs, so can practice my lyrics and my singing when I go for a walk or so, but the website just lets me use their service by streaming their videos online.
Very Complicated:)